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Intermediate Algebra

Julie Miller, Molly O'Neill, Nancy Hyde

Chapter 1

Linear Equations and Inequalities in One Variable - all with Video Answers

Educators

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Section 1

Linear Equations in One Variable 44 Problem Recognition Exercises: Equations versus Expressions

06:20

Problem 1

a. $A n$______ is a statement that indicates that two quantities are equal.
b. $A$ ______ to an equation is a value of the variable that makes the equation a true statement.
c. An equation that can be written in the form $a x+b=c(a \neq 0)$ is called a ______ equation in one variable.
d. A linear equation is also called a ______ - degree equation because the degree on the variable is 1
e. The set of all solutions to an equation is called the ______ ______
f. Two equations are equivalent if they have the same ______ set.
g. A ______ equation is true for some values of the variable, but false for other values.
h. An equation that has no solution is called a ______.
i. The set containing no elements is called the ______and is denoted by ______.
j. An equation that has all real numbers as its solution set is called an ______.

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Ankit Gupta
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00:35

Problem 2

Apply the distributive property.
$$-\frac{1}{2}(6 x-8 y+10)$$

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Ankit Gupta
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00:31

Problem 3

Clear parentheses and combine like terms.
$$8 x-3 y+2 x y-5 x+12 x y$$

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Ankit Gupta
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00:27

Problem 4

Clear parentheses and combine like terms.
$$5 a b+5 a-13-2 a+17$$

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Ankit Gupta
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00:27

Problem 5

Clear parentheses and combine like terms.
$$2(3 z-4)-(z+12)$$

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Ankit Gupta
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00:36

Problem 6

Clear parentheses and combine like terms.
$$-(6 w-5)+3(4 w-5)$$

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Ankit Gupta
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00:33

Problem 7

Label the equation as linear or nonlinear.
$$2 x+1=5$$

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Ankit Gupta
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00:38

Problem 8

Clear parentheses and combine like terms.
$$10=x+6$$

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Ankit Gupta
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01:04

Problem 9

Clear parentheses and combine like terms.
$$x^{2}+7=9$$

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Ankit Gupta
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00:53

Problem 10

Clear parentheses and combine like terms.
$$3+x^{3}-x=4$$

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Ankit Gupta
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00:37

Problem 11

Clear parentheses and combine like terms.
$$-3=x$$

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Ankit Gupta
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00:46

Problem 12

Clear parentheses and combine like terms.
$$5.2-7 x=0$$

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Ankit Gupta
Numerade Educator
01:55

Problem 13

Use substitution to determine which value is the solution to $2 x-1=5$
a. 2
b. 3
c. 0
$\mathbf{d} .-1$

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Ankit Gupta
Numerade Educator
01:40

Problem 14

Use substitution to determine which value is the solution to $2 y-3=-2$
a. 1
b. $\frac{1}{2}$
c. 0
d. $-\frac{1}{2}$

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Ankit Gupta
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00:49

Problem 15

Solve the equation and check the solution.
$$x+7=19$$

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Ankit Gupta
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00:50

Problem 16

Solve the equation and check the solution.
$$-3+y=-28$$

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Ankit Gupta
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00:37

Problem 17

Solve the equation and check the solution.
$$-x=2$$

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Ankit Gupta
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00:43

Problem 18

Solve the equation and check the solution.
$$-t=\frac{3}{4}$$

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Ankit Gupta
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01:23

Problem 19

Solve the equation and check the solution.
$$-\frac{7}{8}=-\frac{5}{6} z$$

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Ankit Gupta
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01:07

Problem 20

Solve the equation and check the solution.
$$-\frac{12}{13}=\frac{4}{3} b$$

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Ankit Gupta
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00:49

Problem 21

Solve the equation and check the solution.
$$\frac{a}{5}=-8$$

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Ankit Gupta
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00:48

Problem 22

Solve the equation and check the solution.
$$\frac{x}{8}=\frac{1}{2}$$

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Ankit Gupta
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01:10

Problem 23

Solve the equation and check the solution.
$$2.53=-2.3 t$$

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Ankit Gupta
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00:58

Problem 24

Solve the equation and check the solution.
$$-4.8=6.1+y$$

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Ankit Gupta
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00:50

Problem 25

Solve the equation and check the solution.
$$p-2.9=3.8$$

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Ankit Gupta
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01:32

Problem 26

Solve the equation and check the solution.
$$-4.2 a=4.494$$

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Ankit Gupta
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00:50

Problem 27

Solve the equation and check the solution.
$$6 q-4=62$$

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Ankit Gupta
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00:49

Problem 28

Solve the equation and check the solution.
$$2 w-15=15$$

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Ankit Gupta
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00:58

Problem 29

Solve the equation and check the solution.
$$4 y-17=35$$

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Ankit Gupta
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00:57

Problem 30

Solve the equation and check the solution.
$$6 z-25=83$$

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Ankit Gupta
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00:55

Problem 31

Solve the equation and check the solution.
$$-b-5=2$$

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Ankit Gupta
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01:03

Problem 32

Solve the equation and check the solution.
$$6=-y+1$$

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Ankit Gupta
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01:09

Problem 33

Solve the equation and check the solution.
$$3(x-6)=2 x-5$$

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Ankit Gupta
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01:14

Problem 34

Solve the equation and check the solution.
$$13 y+4=5(y-4)$$

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Ankit Gupta
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01:46

Problem 35

Solve the equation and check the solution.
$$6-(t+2)=5(3 t-4)$$

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Ankit Gupta
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01:27

Problem 36

Solve the equation and check the solution.
$$1-5(p+2)=2(p+13)$$

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Ankit Gupta
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01:13

Problem 37

Solve the equation and check the solution.
$$6(a+3)-10=-2(a-4)$$

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Ankit Gupta
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01:50

Problem 38

Solve the equation and check the solution.
$$8(b-2)+3 b=-9(b-1)$$

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Ankit Gupta
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02:02

Problem 39

Solve the equation and check the solution.
$$-2[5-(2 z+1)]-4=2(3-z)$$

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Ankit Gupta
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02:01

Problem 40

Solve the equation and check the solution.
$$3[w-(10-w)]=7(w+1)$$

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Ankit Gupta
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02:19

Problem 41

Solve the equation and check the solution.
$$6(-y+4)-3(2 y-3)=-y+5+5 y$$

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Ankit Gupta
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02:20

Problem 42

Solve the equation and check the solution.
$$13+4 w=-5(-w-6)+2(w+1)$$

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Ankit Gupta
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01:28

Problem 43

Solve the equation and check the solution.
$$14-2 x+5 x=-4(-2 x-5)-6$$

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Ankit Gupta
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01:35

Problem 44

Solve the equation and check the solution.
$$8-(p+2)+6 p+7=p+13$$

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Ankit Gupta
Numerade Educator
01:20

Problem 45

Solve the equations.
$$\frac{2}{3} x-\frac{1}{6}=-\frac{5}{12} x+\frac{3}{2}-\frac{1}{6} x$$

AG
Ankit Gupta
Numerade Educator
01:14

Problem 46

Solve the equations.
$$-\frac{1}{2} y+4=-\frac{9}{10} y+\frac{2}{5}$$

AG
Ankit Gupta
Numerade Educator
01:21

Problem 47

Solve the equations.
$$\frac{1}{5}(p-5)=\frac{3}{5} p+\frac{1}{10} p+1$$

AG
Ankit Gupta
Numerade Educator
01:20

Problem 48

Solve the equations.
$$\frac{5}{6}(q+2)=-\frac{7}{9} q-\frac{1}{3}+2$$

AG
Ankit Gupta
Numerade Educator
01:29

Problem 49

Solve the equations.
$$\frac{3 x-7}{2}+\frac{3-5 x}{3}=\frac{3-6 x}{5}$$

AG
Ankit Gupta
Numerade Educator
01:34

Problem 50

Solve the equations.
$$\frac{2 y-4}{5}=\frac{5 y+13}{4}+\frac{y}{2}$$

AG
Ankit Gupta
Numerade Educator
01:23

Problem 51

Solve the equations.
$$\frac{4}{3}(2 q+6)-\frac{5 q-6}{6}-\frac{q}{3}=0$$

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Ankit Gupta
Numerade Educator
01:56

Problem 52

Solve the equations.
$$\frac{-3 a+9}{15}-\frac{2 a-5}{5}-\frac{a+2}{10}=0$$

AG
Ankit Gupta
Numerade Educator
00:48

Problem 53

Solve the equations.
$$6.3 w-1.5=4.8$$

AG
Ankit Gupta
Numerade Educator
01:20

Problem 54

Solve the equations.
$$0.2 x+53.6=x$$

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Ankit Gupta
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01:30

Problem 55

Solve the equations.
$$0.75(m-2)+0.25 m=0.5$$

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Ankit Gupta
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01:13

Problem 56

Solve the equations.
$$0.4(n+10)+0.6 n=2$$

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Ankit Gupta
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00:49

Problem 57

What is a conditional equation?

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Ankit Gupta
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01:50

Problem 58

Explain the difference between a contradiction and an identity.

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Ankit Gupta
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00:52

Problem 59

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$4 x+1=2(2 x+1)-1$$

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Ankit Gupta
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00:53

Problem 60

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$3 x+6=3 x$$

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Ankit Gupta
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01:10

Problem 61

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$-11 x+4(x-3)=-2 x-12$$

AG
Ankit Gupta
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00:47

Problem 62

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$5(x+2)-7=3$$

AG
Ankit Gupta
Numerade Educator
00:52

Problem 63

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$2 x-4+8 x=7 x-8+3 x$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 64

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set.
$$-7 x+8+4 x=-3(x-3)-1$$

AG
Ankit Gupta
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00:32

Problem 65

Solve the equations.
$$-5 b+9=-71$$

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Ankit Gupta
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00:26

Problem 66

Solve the equations.
$$-3 x+18=-66$$

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Ankit Gupta
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00:28

Problem 67

Solve the equations.
$$16=-10+13 x$$

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Ankit Gupta
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00:28

Problem 68

Solve the equations.
$$15=-12+9 x$$

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Ankit Gupta
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00:30

Problem 69

Solve the equations.
$$10 c+3=-3+12 c$$

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Ankit Gupta
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00:27

Problem 70

Solve the equations.
$$2 w+21=6 w-7$$

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Ankit Gupta
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00:55

Problem 71

Solve the equations.
$$12 b-8 b-8+13=4 b+6-1$$

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Ankit Gupta
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00:46

Problem 72

Solve the equations.
$$4 z+2-3 z+5=3+z+4$$

AG
Ankit Gupta
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00:49

Problem 73

Solve the equations.
$$5(x-2)-2 x=3 x+7$$

AG
Ankit Gupta
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00:31

Problem 74

Solve the equations.
$$2 x+3(x-5)=15$$

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Ankit Gupta
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00:56

Problem 75

Solve the equations.
$$\frac{c}{2}-\frac{c}{4}+\frac{3 c}{8}=1$$

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Ankit Gupta
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01:11

Problem 76

Solve the equations.
$$\frac{d}{5}-\frac{d}{10}+\frac{5 d}{20}=\frac{7}{10}$$

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Ankit Gupta
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01:19

Problem 77

Solve the equations.
$$0.75(8 x-4)=\frac{2}{3}(6 x-9)$$

AG
Ankit Gupta
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00:46

Problem 78

Solve the equations.
$$-\frac{1}{2}(4 z-3)=-z$$

AG
Ankit Gupta
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00:53

Problem 79

Solve the equations.
$$7(p+2)-4 p=3 p+14$$

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Ankit Gupta
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00:38

Problem 80

Solve the equations.
$$6(z-2)=3 z-8+3 z$$

AG
Ankit Gupta
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01:08

Problem 81

Solve the equations.
$$4[3+5(3-b)+2 b]=6-2 b$$

AG
Ankit Gupta
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01:06

Problem 82

Solve the equations.
$$\frac{1}{3}(x+3)-\frac{1}{6}=\frac{1}{6}(2 x+5)$$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 83

Solve the equations.
$$3-\frac{3}{4} x=3\left(3-\frac{1}{4} x\right)$$

AG
Ankit Gupta
Numerade Educator
00:56

Problem 84

Solve the equations.
$$\frac{9}{5}-8 w=8\left(\frac{3}{5}-w\right)$$

AG
Ankit Gupta
Numerade Educator
01:09

Problem 85

Solve the equations.
$$\frac{5}{4}+\frac{y-3}{8}=\frac{2 y+1}{2}$$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 86

Solve the equations.
$$\frac{2}{3}-\frac{x+2}{6}=\frac{5 x-2}{2}$$

AG
Ankit Gupta
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01:09

Problem 87

Solve the equations.
$$\frac{2 y-9}{10}+\frac{3}{2}=y$$

AG
Ankit Gupta
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01:11

Problem 88

Solve the equations.
$$\frac{2}{3} x-\frac{5}{6} x-3=\frac{1}{2} x-5$$

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Ankit Gupta
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01:25

Problem 89

Solve the equations.
$$0.48 x-0.08 x=0.12(260-x)$$

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Ankit Gupta
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01:25

Problem 90

Solve the equations.
$$0.07 w+0.06(140-w)=90$$

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Ankit Gupta
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01:41

Problem 91

Solve the equations.
$$0.5 x+0.25=\frac{1}{3} x+\frac{5}{4}$$

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Ankit Gupta
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01:01

Problem 92

Solve the equations.
$$0.2 b+\frac{1}{3}=\frac{7}{15}$$

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Ankit Gupta
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01:33

Problem 93

Solve the equations.
$$0.3 b-1.5=0.25(b+2)+0.05 b$$

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Ankit Gupta
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00:55

Problem 94

Solve the equations.
$$0.7(a-1)=0.25+0.7 a$$

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Ankit Gupta
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01:30

Problem 95

Solve the equations.
$$-\frac{7}{8} y+\frac{1}{4}=\frac{1}{2}\left(5-\frac{3}{4} y\right)$$

AG
Ankit Gupta
Numerade Educator
01:04

Problem 96

Solve the equations.
$$5 x-(8-x)=2[-4-(3+5 x)-13]$$

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Ankit Gupta
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01:27

Problem 97

A power company charges 0.12 dollar per kilowatt-hour (kWh) and 14.89 dollar in monthly taxes. The monthly charge $C$ (in $\$$ ) is given by $C=0.12 h+14.89$ where $h$ is the number of kilowatt-hours used. If a family's bill comes to 137.77 dollar determine the number of kilowatt-hours used.

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Ankit Gupta
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01:12

Problem 98

For a student's first semester at college, the college charges 105 dollar per credit-hour plus a one-time $\$ 50$ admissions fee. The cost $C$ (in $\mathrm{S}$ ) for the first semester is given by $C=105 h+50$ where $h$ is the number of credit-hours taken. If a student is billed 1415 dollar, how many credit-hours is she taking?

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Ankit Gupta
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01:28

Problem 99

a. Simplify the expression. $-2(y-1)+3(y+2)$
b. Solve the equation. $-2(y-1)+3(y+2)=0$
c. Explain the difference between simplifying an expression and solving an equation.

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Ankit Gupta
Numerade Educator
01:50

Problem 100

a. Simplify the expression. $4 w-8(2+w)$
b. Solve the equation. $4 w-8(2+w)=0$
c. Explain the difference between simplifying an expression and solving an equation.

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Ankit Gupta
Numerade Educator