Intermediate Algebra for College Students

Allen R. Angel; Dennis C. Runde

Chapter 2

Equations and Inequalities - all with Video Answers

Educators

Section 1

Solving Linear Equations

Problem 1

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
The parts that are added in an algebraic expression are called the ________ of the expression.

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 1

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
The goal of the addition method is to obtain an equation that contains only one ______

Rylie Howey

Numerade Educator

Problem 2

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
Terms that have identical variable parts are called _______ terms.

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 2

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
For a system of equations with three equations and three variables, the solution is an __________ triple.

Tanishq Gupta

Numerade Educator

Problem 3

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
The goal in solving equations is _________ to the variable on one side of the equation.

Satish Yadav

Numerade Educator

Problem 3

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
A system of equations that has an infinite number of solutions is $a(n)$ _________ system.

Tanishq Gupta

Numerade Educator

Problem 4

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
We can eliminate fractions from an equation by multiplying both sides of the equation by the ___________ common denominator.

Satish Yadav

Numerade Educator

Problem 4

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
A system of equations that has no solution is a(n) __________ system.

Tanishq Gupta

Numerade Educator

Problem 5

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
An equation that is always true is known as $a(n)$ _________

AG

Ankit Gupta

Numerade Educator

Problem 5

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
A system of equations that has at least one solution is $a(n)$ ________ system.

Tanishq Gupta

Numerade Educator

Problem 6

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
An equation that is true for only specific values of the variable is known as $a(n)$ _________ equation.

Satish Yadav

Numerade Educator

Problem 6

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
The ________solution to a system of two linear equations is located at the intersection point of the graphs of the equations.

Tanishq Gupta

Numerade Educator

Problem 7

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
An equation that is never true is known as a(n) _________

AG

Ankit Gupta

Numerade Educator

Problem 7

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
The lines that represent the equations in an inconsistent system of linear equations are ____________ lines.

Rylie Howey

Numerade Educator

Problem 8

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
The ___________ of a term is the sum of the exponents on the variables in the term.

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 8

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
The lines that represent the equations in a dependent system of linear equations are the _________ line.

Rylie Howey

Numerade Educator

Problem 9

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
The symbol _____________ is used to indicate the solution set of a contradiction.

AG

Ankit Gupta

Numerade Educator

Problem 9

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
For a consistent linear system with two equations and two variables, a solution is an ordered ___________

Rylie Howey

Numerade Educator

Problem 10

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { conditional } & \varnothing & \text { like } & \text { identity least } \\ \text { terms } & \text { contradiction } & \text { degree } & \text { unlike } & \text { isolate }\end{array}$
The symbol ___________ is used to indicate the solution set of an identity.

AG

Ankit Gupta

Numerade Educator

Problem 10

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\begin{array}{lllll}\text { unique } & \text { dependent } & \text { consistent } & \text { inconsistent } & \text { intersecting } \\ \text { variable } & \text { perpendicular } & \text { parallel } & \text { same } & \text { pair }\end{array}$
The lines that represent the equations in a consistent system of linear equations with a unique solution are _________ lines.

Tanishq Gupta

Numerade Educator

Problem 11

Name each indicated property.
If $-7=x$, then $x=-7$

Robert Leedy

Numerade Educator

Problem 11

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations.
$$
\text { - } y=3 x-1
$$
$$
y=2 x+3
$$
a) $(0,3)$
b) $(4,11)$

Catheryn Taylor

Catheryn Taylor

Numerade Educator

Problem 12

Name each indicated property.
If $11=2 x-3 y$, then $2 x-3 y=11$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 12

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations.
$$
4 x+3 y=11
$$
$$
y=\frac{3}{2} x-2
$$
a) $(2,1)$
b) $(0,-2)$

James Kiss

Numerade Educator

Problem 13

Name each indicated property.
If $x=y$ and $y=-4$, then $x=-4$.

Julie Silva

Numerade Educator

Problem 13

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations.
$$
\begin{aligned}
&x+2 y=4 \\
&y=-\frac{1}{2} x+2
\end{aligned}
$$
a) $(2,1)$
b) $(4,0)$

Melissa Barry

Numerade Educator

Problem 14

Name each indicated property.
If $3 x-7=y$, and $y=5 x+3$, then $3 x-7=5 x+3$

AG

Ankit Gupta

Numerade Educator

Problem 14

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations.
$$
y=\frac{x}{3}-\frac{7}{3}
$$
$$
5 x-35=15 y
$$
a) $(1,-2)$
b) $(7,0)$

Raushan Kumar

Numerade Educator

Problem 15

Name each indicated property. $a+c=a+c$

Vicki Stebbins

Numerade Educator

Problem 15

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations.
$$
\begin{aligned}
&x+2 y-z=-5 \\
&2 x-y+2 z=8 \\
&3 x+3 y+4 z=5
\end{aligned}
$$
a) $(3,1,-2)$
b) $(1,-2,2)$

James Kiss

Numerade Educator

Problem 16

Name each indicated property. $14=14$

J Alessandro Briseño-Tapia

J Alessandro Briseño-Tapia

Numerade Educator

Problem 16

Determine which, if any, of the given ordered pairs or ordered triples satisfy the system of linear equations. $$
\begin{aligned}
&4 x+y-3 z=1 \\
&2 x-2 y+6 z=11 \\
&-6 x+3 y+12 z=-4
\end{aligned}
$$
a) $(2,-1,-2)$
b) $\left(\frac{1}{2}, 2,1\right)$

James Kiss

Numerade Educator

Problem 17

Name each indicated property.If $x=8$, then $x-8=8-8$.

J Alessandro Briseño-Tapia

J Alessandro Briseño-Tapia

Numerade Educator

Problem 17

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $x+y=-2$
$3 y+12=-6 x$

Supratim Roy

Numerade Educator

Problem 18

Name each indicated property. If $\frac{2}{3} x=4$, then $\frac{3}{2}\left(\frac{2}{3} x\right)=\frac{3}{2}(4)$

Eva R

Numerade Educator

Problem 18

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $2 x-4 y=5$
$x-2 y=1$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 19

Name each indicated property. If $5 x=4$, then $\frac{1}{5}(5 x)=\frac{1}{5}(4)$

Julie Silva

Numerade Educator

Problem 19

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $3 x-3 y=9$
$2 x-2 y=-4$

Supratim Roy

Numerade Educator

Problem 20

Name each indicated property. If $a+2=4$, then $a+2-2=4-2$

Zach Steedman

Numerade Educator

Problem 20

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $2 x=3 y+4$
$6 x-9 y=12$

Supratim Roy

Numerade Educator

Problem 21

Name each indicated property. If $\frac{t}{4}+\frac{1}{3}=\frac{5}{6}$, then $12\left(\frac{t}{4}+\frac{1}{3}\right)=12\left(\frac{5}{6}\right)$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 21

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $\frac{x}{3}+\frac{y}{4}=1$
$4 x+3 y=12$

Ian Maurer

Numerade Educator

Problem 22

Name each indicated property. If $7 x-4=10$, then $7 x-4+4=10+4$

J Alessandro Briseño-Tapia

J Alessandro Briseño-Tapia

Numerade Educator

Problem 22

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $\frac{x}{3}+\frac{y}{4}=1$
$2 x-3 y=12$

Dale Sanford

Numerade Educator

Problem 23

Name each indicated property. If $x+3=7$, then $x=4$.

Robert Leedy

Numerade Educator

Problem 23

Determine the solution to each system of equations graphically. $y=-5 x+5$
$y=2 x-2$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 24

Name each indicated property. If $5 x=35$ then $x=7$.

Julie Silva

Numerade Educator

Problem 24

Determine the solution to each system of equations graphically.
$y=2 x+8$
$y=-3 x-12$

Ian Maurer

Numerade Educator

Problem 25

Give the degree of each term. $x$

Cory Kuzinski

Numerade Educator

Problem 25

Determine the solution to each system of equations graphically. $y=-\frac{1}{3} x-1$
$2 x-3 y=12$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 26

Give the degree of each term. $5 y$

Cory Kuzinski

Numerade Educator

Problem 26

Determine the solution to each system of equations graphically. $y=-2 x-1$
$x+2 y=4$

Haley Mortell

Numerade Educator

Problem 27

Give the degree of each term. $5 c^{3}$

Cory Kuzinski

Numerade Educator

Problem 27

Determine the solution to each system of equations graphically. $x+y=3$
$x-y=1$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 28

Give the degree of each term. $-6 y^{2}$

Jeyasree R T

Numerade Educator

Problem 28

Determine the solution to each system of equations graphically. $4 x-y=9$
$x-3 y=16$

AG

Ankit Gupta

Numerade Educator

Problem 29

Give the degree of each term. $3 a b$

Cory Kuzinski

Numerade Educator

Problem 29

Determine the solution to each system of equations graphically. $2 x+3 y=6$
$4 x=-6 y+12$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 30

Give the degree of each term. $-2 x y$

Cory Kuzinski

Numerade Educator

Problem 30

Determine the solution to each system of equations graphically. $2 x-5 y=10$
$y=\frac{2}{5} x-2$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 31

Give the degree of each term. 6

Cory Kuzinski

Numerade Educator

Problem 31

Determine the solution to each system of equations graphically. $y=4 x-1$
$3 y=12 x+9$

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 32

Give the degree of each term. $-3$

Cory Kuzinski

Numerade Educator

Problem 32

Determine the solution to each system of equations graphically. $x-\frac{1}{2} y=-2$
$2 y=4 x-6$

Ian Maurer

Numerade Educator

Problem 33

Give the degree of each term. $\frac{1}{2} x^{4} y$

Cory Kuzinski

Numerade Educator

Problem 33

Determine the solution to each system of equations graphically. $5 x+3 y=13$
$x=2$

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 34

Give the degree of each term. $18 p^{2} q^{3}$

Cory Kuzinski

Numerade Educator

Problem 34

Determine the solution to each system of equations graphically.$3 x-4 y=2$
$y=-2$

Naresh Bagrecha

Naresh Bagrecha

Numerade Educator

Problem 35

Give the degree of each term. $5 a^{2} b^{4} c$

AG

Ankit Gupta

Numerade Educator

Problem 35

Determine the solution to each system of equations by substitution. $2 x-7 y=-1$
$y=-2 x+7$

Marcial Vargas

Numerade Educator

Problem 36

Give the degree of each term. $3 x^{5} y^{6} z$

Cory Kuzinski

Numerade Educator

Problem 36

Determine the solution to each system of equations by substitution. $4 x-5 y=3$
$y=-6 x+13$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 37

Give the degree of each term. $11 a^{2} c^{5} d^{10}$

Cory Kuzinski

Numerade Educator

Problem 37

Determine the solution to each system of equations by substitution. $x=4 y-1$
$3 x-2 y=7$

Ma. Theresa Alin

Ma. Theresa Alin

Numerade Educator

Problem 38

Give the degree of each term. $-2 x^{4} y^{7} z^{8}$

Cory Kuzinski

Numerade Educator

Problem 38

Determine the solution to each system of equations by substitution. $4 x=3 y+17$
$x=-2 y-4$

Erika Bustos

Numerade Educator

Problem 39

Simplify each expression. If an expression cannot be simplified, so state. $-2 x^{2}-5 x+7 x-3$

Tyler Moulton

Numerade Educator

Problem 39

Determine the solution to each system of equations by substitution. $x=2 y+3$
$y=x$

Angela Guo

Numerade Educator

Problem 40

Simplify each expression. If an expression cannot be simplified, so state. $2 a^{2}-4 a b+5 a b-10 b^{2}$

Peggy Radtke

Numerade Educator

Problem 40

Determine the solution to each system of equations by substitution.
$x=2 y+3$
$y=x$

Angela Guo

Numerade Educator

Problem 41

Simplify each expression. If an expression cannot be simplified, so state. $w^{3}+w^{2}-w+1$

Joshua Fischbach

Joshua Fischbach

Numerade Educator

Problem 41

Determine the solution to each system of equations by substitution.
$a+3 b=5$
$2 a-b=3$

Carson Merrill

Numerade Educator

Problem 42

Simplify each expression. If an expression cannot be simplified, so state. $k^{3}-3 k^{2}-11 k+1$

Jonathan Turovsky

Jonathan Turovsky

Numerade Educator

Problem 42

Determine the solution to each system of equations by substitution. $a+b=3$
$0.05 a+0.3 b=0.6$

Palitha Reddy

Numerade Educator

Problem 43

Simplify each expression. If an expression cannot be simplified, so state. $10.6 c^{2}-2.3 c+5.9 c-1.9 c^{2}$

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 44

Simplify each expression. If an expression cannot be simplified, so state. $4.3-3.2 x-2(x-2)$

Matt Gibson

Numerade Educator

Problem 45

Simplify each expression. If an expression cannot be simplified, so state. $5 a-2 b+3 c+9 d-8$

Emily Himsel

Numerade Educator

Problem 46

Simplify each expression. If an expression cannot be simplified, so state. $7 x^{3} y^{2}+11 x^{2} y^{3}$

Jeyasree R T

Numerade Educator

Problem 47

Simplify each expression. If an expression cannot be simplified, so state. $8 p q-9 p q+p+q$

Amy Jiang

Numerade Educator

Problem 48

Simplify each expression. If an expression cannot be simplified, so state. $b+b^{2}-4 b+b^{2}+3 b$

Amy Jiang

Numerade Educator

Problem 49

Simplify each expression. If an expression cannot be simplified, so state. $12\left(\frac{1}{6}+\frac{d}{4}\right)+5 d$

Ashley High

Numerade Educator

Problem 50

Simplify each expression. If an expression cannot be simplified, so state. $60\left(\frac{7}{15} x-\frac{3}{4}\right)-2 x$

Ali Soave

Numerade Educator

Problem 51

Simplify each expression. If an expression cannot be simplified, so state. $8\left(\frac{7}{8} x+3\right)+5 x-7$

Caleb Huber

Numerade Educator

Problem 52

Simplify each expression. If an expression cannot be simplified, so state. $-4\left(\frac{3}{4} x-5\right)+7 x-1$

JL

Jacob Lombardo

Numerade Educator

Problem 53

Simplify each expression. If an expression cannot be simplified, so state. $4-[6(3 x+2)-x]+4$

Nick Johnson

Numerade Educator

Problem 54

Simplify each expression. If an expression cannot be simplified, so state. $-9+3[4(2 x-3)-5 x]+2 x$

Susan Cooper

Numerade Educator

Problem 55

Simplify each expression. If an expression cannot be simplified, so state. $9 x-[3 x-(5 x-4 y)]-2 y$

Joshua Fischbach

Joshua Fischbach

Numerade Educator

Problem 56

Simplify each expression. If an expression cannot be simplified, so state. $-2[3 x-(2 y-1)-5 x]+y$

Julie Silva

Numerade Educator

Problem 57

Simplify each expression. If an expression cannot be simplified, so state. $5 b-\{7[2(3 b-2)-(4 b+9)]-2\}$

Brandon Fox

Numerade Educator

Problem 58

Simplify each expression. If an expression cannot be simplified, so state. $2\{[3 a-(2 b-5 a)]-3(2 a-b)\}$

Amy Jiang

Numerade Educator

Problem 59

Simplify each expression. If an expression cannot be simplified, so state. $-\left\{[2 r s-3(r+2 s)]-2\left(2 r^{2}-s\right)\right\}$

Amy Jiang

Numerade Educator

Problem 60

Simplify each expression. If an expression cannot be simplified, so state. $-[-2 t+3(2 u-4)+v]-3\{-2[t-5(u+1)+v]\}$

Julie Silva

Numerade Educator

Problem 61

Solve each equation. $5 a-1=14$

Bailey Radel

Numerade Educator

Problem 62

Solve each equation. $-7 x+3=17$

Brandon Fox

Numerade Educator

Problem 63

Solve each equation. $-8 x+7+3 x=-3$

Ian Maurer

Numerade Educator

Problem 64

Solve each equation. $7 x-6-5 x=-8$

Susan Cooper

Numerade Educator

Problem 65

Solve each equation. $5 s-3=2 s+6$

Karuna Ramroop

Numerade Educator

Problem 66

Solve each equation. $8 w+7=-3 w-15$

AG

Ankit Gupta

Numerade Educator

Problem 67

Solve each equation. $4 x-5=2(x+5)$

Matthew Biollo

Numerade Educator

Problem 68

Solve each equation. $3(y-7)=5 y-10$

Brandon Fox

Numerade Educator

Problem 69

Solve each equation. $-3(t-5)=2(t-5)$

Melissa Lupinacci

Melissa Lupinacci

Numerade Educator

Problem 70

Solve each equation. $4(2 x-4)=-2(x+3)$

James Kiss

Numerade Educator

Problem 71

Solve each equation. $3 x+4(2-x)=4 x+5$

Bailey Radel

Numerade Educator

Problem 72

Solve each equation. $7 z-3(2 z-5)=8 z+11$

Chandler Austin

Chandler Austin

Numerade Educator

Problem 73

Solve each equation. $2-(x+5)=4 x-8$

RR

Roba Roba

Numerade Educator

Problem 74

Solve each equation. $3 k+7=4-(9-k)$

Palitha Reddy

Numerade Educator

Problem 75

Solve each equation. $p-(p+4)=4(p-1)+2 p$

Nick Johnson

Numerade Educator

Problem 76

Solve each equation. $q-(-2 q+3)=-5(q-3)-18$

Jake Zanazzi

Numerade Educator

Problem 77

Solve each equation. $-3(y-1)+2 y=4(y-3)$

Amy Jiang

Numerade Educator

Problem 78

Solve each equation. $2(3 z+2)-4 z=5(z+1)-13$

Brandon Fox

Numerade Educator

Problem 79

Solve each equation. $6-(n+3)=3 n+5-2 n$

Rupsa Sarkar

Numerade Educator

Problem 80

Solve each equation. $8-3(2 a-4)=5+3 a-4 a$

Cory Kuzinski

Numerade Educator

Problem 81

Solve each equation. $4(2 x-2)-3(x+7)=-4$

Julie Silva

Numerade Educator

Problem 82

Solve each equation. $-2(3 w+6)-(4 w-3)=21$

Nick Johnson

Numerade Educator

Problem 83

Solve each equation. $-4(3-4 x)-2(x-1)=12 x$

Sherrie Fenner

Numerade Educator

Problem 84

Solve each equation. $3(2 x-4)+3(x+1)=9$

Ashley Volpe

Numerade Educator

Problem 85

Solve each equation. $5(a+3)-a=-(4 a-6)+1$

RR

Roba Roba

Numerade Educator

Problem 86

Solve each equation. $-4(2 z-6)=-3(z-4)+z$

Jake Zanazzi

Numerade Educator

Problem 87

Solve each equation. $-2[8-(4-w)]-8=4(w+5)$

Julie Silva

Numerade Educator

Problem 88

Solve each equation. $3[6-(h+2)]-6=4(-h+7)$

Melissa Stefan

Numerade Educator

Problem 89

Solve each equation. $4\{2-[3(c+1)-2(c+1)]\}=-2 c$

Catt Huth

Numerade Educator

Problem 90

Solve each equation. $3\{[(x-2)+4 x]-(x-3)\}=4-(x-12)$

Sherrie Fenner

Numerade Educator

Problem 91

Solve each equation. $-\{4(d+3)-5[3 d-2(2 d+7)]-8\}=-10 d-6$

Brandon Fox

Numerade Educator

Problem 92

Solve each equation. $-3(6-4 x)=4-\{5 x-[6 x-(4 x-(3 x+2))]\}$

Xiaomeng Zhang

Numerade Educator

Problem 93

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{d}{5}=-7$

Brandon Fox

Numerade Educator

Problem 94

Solve each equation. Leave your answer as a fraction if it is not an integer value. $-\frac{q}{8}=5$

Teresa Fuston

Numerade Educator

Problem 95

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{4 x-2}{3}=-6$

Erika Bustos

Numerade Educator

Problem 96

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{7 m+9}{6}=5$

Brandon Fox

Numerade Educator

Problem 97

Solve each equation. Leave your answer as a fraction if it is not an integer value. $4-\frac{3}{4} a=7$

Ashley Volpe

Numerade Educator

Problem 98

Solve each equation. Leave your answer as a fraction if it is not an integer value. $-2=-\frac{1}{3} x+4$

Shaza Hammoud

Numerade Educator

Problem 99

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{5}{14} x+\frac{1}{2}=\frac{11}{7}$

Erika Bustos

Numerade Educator

Problem 100

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{7}{15} x-\frac{1}{5}=\frac{5}{3}$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 101

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{7}{15} x+\frac{3}{5}=\frac{1}{3} x+\frac{5}{3}$

Jake Zanazzi

Numerade Educator

Problem 102

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{5}{14} x+\frac{3}{7}=\frac{1}{7} x-\frac{3}{2}$

Erika Bustos

Numerade Educator

Problem 103

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{2}{3} z-5=\frac{z}{6}+1$

Alison Rodriguez

Alison Rodriguez

Numerade Educator

Problem 104

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{1}{2} x+2=\frac{1}{8} x-1$

Victor Salazar

Numerade Educator

Problem 105

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{7}{9} m+\frac{3}{10}=\frac{2}{15} m-\frac{5}{18}$

Brandon Fox

Numerade Educator

Problem 106

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{3}{4} n-\frac{4}{21}=\frac{5}{28} n-\frac{7}{12}$

Angela Guo

Numerade Educator

Problem 107

Solve each equation. Leave your answer as a fraction if it is not an integer value. $x+6=-\frac{2}{3}(x+1)$

Emily Brown

Numerade Educator

Problem 108

Solve each equation. Leave your answer as a fraction if it is not an integer value. $x-2=\frac{3}{4}(x+4)$

Dale Sanford

Numerade Educator

Problem 109

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{1}{2}(x-2)=\frac{1}{3}(x+2)$

Teresa Fuston

Numerade Educator

Problem 110

Solve each equation. Leave your answer as a fraction if it is not an integer value. $\frac{3}{4}(x-5)=\frac{2}{3}(x-7)$

Erika Bustos

Numerade Educator

Problem 111

Solve each equation. If necessary, round answers to the nearest hundredth. $0.4 n+4.7=5.1 n$

Victor Salazar

Numerade Educator

Problem 112

Solve each equation. If necessary, round answers to the nearest hundredth. $0.8 x-4=2.1 x+3.2$

Ashley High

Numerade Educator

Problem 113

Solve each equation. If necessary, round answers to the nearest hundredth. $1.69 x-3.1=0.05-5.9 x$

Amy Jiang

Numerade Educator

Problem 114

Solve each equation. If necessary, round answers to the nearest hundredth. $4.2 x+9.7=-3.95 x-6.8$

Teresa Fuston

Numerade Educator

Problem 115

Solve each equation. If necessary, round answers to the nearest hundredth. $4.7 x-3.6(x-1)=4.9$

Ashley High

Numerade Educator

Problem 116

Solve each equation. If necessary, round answers to the nearest hundredth. $6.1 p-4.5(3-2 p)=15.7$

Brandon Fox

Numerade Educator

Problem 117

Solve each equation. If necessary, round answers to the nearest hundredth. $0.6(500-2.4 x)=3.6(2 x-4000)$

Amrita Bhasin

Numerade Educator

Problem 118

Solve each equation. If necessary, round answers to the nearest hundredth. $0.6(14 x-8000)=-0.4(20 x+12,000)+20.6 x$

Amrita Bhasin

Numerade Educator

Problem 119

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $3(y+3)-4(2 y-7)=-5 y+2$

Vinnu M

Numerade Educator

Problem 120

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $7 x+5-5(x-3)=5(x+4)-3 x$

AG

Ankit Gupta

Numerade Educator

Problem 121

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $7+3(x-2)+8 x=6(x+1)+2 x-9$

Suzanne Harwood

Suzanne Harwood

Numerade Educator

Problem 122

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $-5(c+3)+4(c-2)=2(c+2)$

MA

Mohamed Abd El Aziz

Numerade Educator

Problem 123

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $6(x-1)=-3(2-x)+3 x$

Vinnu M

Numerade Educator

Problem 124

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $4(2-3 x)=-[6 x-(8-6 x)]$

AG

Ankit Gupta

Numerade Educator

Problem 125

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $4-\left(\frac{2}{3} x+2\right)=2\left(-\frac{1}{3} x+1\right)$

Deepak Kumar

Numerade Educator

Problem 126

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $7-\left(\frac{1}{2} x+4\right)=3\left(-\frac{1}{6} x+2\right)$

Suzanne Harwood

Suzanne Harwood

Numerade Educator

Problem 127

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $0.8 z-0.3(z+10)=0.5(z+1)$

Jake Zanazzi

Numerade Educator

Problem 128

Determine the solution set for each exercise. Then indicate whether the equation is conditional, an identity, or a contradiction. $0.6(z+5)-0.5(z+2)=0.1(z-23)$

Jake Zanazzi

Numerade Educator

Problem 129

Population Density The population density of the United States has been steadily increasing since 2000 . The population density of the United States can be estimated using the equation
$$
P=0.82 t+78.5
$$
where $P$ is the population density, measured in people per square mile, and $t$ is the number of years since 2000. Use $t=1$ for 2001, $t=2$ for 2002, and so on. If the population density continues to increase at its current rate,
a) determine the population density of the United States in $2018 .$
b) during what year will the population density of the United States reach 100 people per square mile?

Julie Silva

Numerade Educator

Problem 130

Sleeping Babies Dr. Richard Ferber, a pediatric sleep expert, has developed a method* to help children, 6 months of age or older, sleep through the night. Often called "Ferberizing," it calls for parents to wait for increasing lengths of time before entering the child's room at night to comfort the crying child. The suggested waiting time depends on how many nights the parents have been using the method and may be found using the equation
$$
w=5 n+5
$$
where $W$ is the waiting time in minutes and $n$ is the number of the night. For example, on the first night, $n=1$, on the second night, $n=2$, and so on.
a) How long should parents wait on the first night?
b) How long should parents wait on the fourth night?
c) On what night should parents wait 30 minutes?
d) On what night should parents wait 40 minutes?

Emily Schein

Numerade Educator

Problem 131

Salsa Business Delbert makes homemade salsa and sells it at his roadside produce stand. Delbert's weekly cost for making salsa can be determined using the equation $C=2.75 j+40$, where $C$ represents the cost in dollars and $j$ represents the number of jars of salsa made.
a) Determine Delbert's weekly cost for making 20 jars of salsa.
b) Determine Delbert's weekly cost for making 50 jars of salsa.
c) How many jars of salsa would Delbert need to make for his cost to be $\$ 205$ ?

Teresa Fuston

Numerade Educator

Problem 132

Homemade Pies Janet bakes homemade pies and sells them at the local farmers market. Janet's weekly profit from the pies can be found using the formula $P=3.75 x-33.75$. In this equation $P$ represents the profit in dollars and $x$ represents the number of pies sold.
a) Determine Janet's weekly profit if she sells 50 pies.
b) How many pies would Janet have to sell in one week in order to break even $(P=0)$ ?
c) How many pies would Janet have to sell in one week in order to have a profit of $\$ 300 ?$

Brian Schumeyer

Brian Schumeyer

Numerade Educator

Problem 133

Solve each equation for the given symbol. Assume that the symbol you are solving for represents the variable and that all other symbols represent nonzero real numbers. See Example $11 .$ Solve $* \Delta-\square=\odot$ for $\Delta$.

Jennifer Fernéz

Jennifer Fernéz

Numerade Educator

Problem 134

Solve each equation for the given symbol. Assume that the symbol you are solving for represents the variable and that all other symbols represent nonzero real numbers. See Example $11 .$ Solve $\Delta(\odot+\square)=\otimes$ for $\Delta$

Jennifer Fernéz

Jennifer Fernéz

Numerade Educator

Problem 135

Solve each equation for the given symbol. Assume that the symbol you are solving for represents the variable and that all other symbols represent nonzero real numbers. See Example $11 .$ Solve $\odot \square+\Delta=\otimes$ for $\odot$.

Sherrie Fenner

Numerade Educator

Problem 136

Solve each equation for the given symbol. Assume that the symbol you are solving for represents the variable and that all other symbols represent nonzero real numbers. See Example $11 .$ Solve $\Delta(\odot+\square)=\otimes$ for $\square$.

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 137

Consider the equation $2 x=5$. Give three equivalent equations. Explain why the equations are equivalent.

Vinnu M

Numerade Educator

Problem 138

Consider the equation $x=4$. Give three equivalent equations. Explain why the equations are equivalent.

Cory Kuzinski

Numerade Educator

Problem 139

Make up an equation that is a contradiction. Explain how you created the contradiction.

Julie Silva

Numerade Educator

Problem 140

Make up an equation that is an identity. Explain how you created the equation.

Julie Silva

Numerade Educator

Problem 141

Create an equation with two terms to the left of the equals sign and three terms to the right of the equals sign that is equivalent to the equation $\frac{1}{2} p+3=6$.

Courtney Solomon

Courtney Solomon

Numerade Educator

Problem 142

Create an equation with three terms to the left of the equals sign and two terms to the right of the equals sign that is equivalent to the equation $3 m+1=m+5$.

AG

Ankit Gupta

Numerade Educator

Problem 143

Consider the equation $2(a+5)+n=4 a-8$. What real number must $n$ be for the solution of the equation to be $-2$ ? Explain how you determined your answer.

James Chok

Numerade Educator

Problem 144

Consider the equation $-3(x+2)+5 x+12=n$. What real number must $n$ be for the solution of the equation to be 6? Explain how you determined your answer.

Ali Soave

Numerade Educator

Problem 145

a) Explain how to determine the absolute value of a number.
b) Write the definition of absolute value.

Michael Jacobsen

Michael Jacobsen

Numerade Educator

Problem 146

Evaluate.
a) $-3^{2}$
b) $(-3)^{2}$

Erika Bustos

Numerade Educator

Problem 147

Evaluate.
$\sqrt[3]{-125}$

Julie Silva

Numerade Educator

Problem 148

Evaluate.
$\left(-\frac{2}{7}\right)^{2}$

Erika Bustos

Numerade Educator