Algebra A Combined Function

Elayn Martin-Gay

Chapter 2 Equations, Inequalities, and Problem Solving - all with Video Answers

Educators

Section 1

The Addition Property of Equality

01:08

Problem 1

Solve each equation. Check each solution.
$$
x+7=10
$$

Julie Silva

Numerade Educator

00:59

Problem 2

Solve each equation. Check each solution.
$$
x+14=25
$$

Julie Silva

Numerade Educator

01:04

Problem 3

Solve each equation. Check each solution.
$$
x-2=-4
$$

Julie Silva

Numerade Educator

00:55

Problem 4

Solve each equation. Check each solution.
$$
y-9=1
$$

Julie Silva

Numerade Educator

01:03

Problem 5

Solve each equation. Check each solution.
$$
-11=3+x
$$

Julie Silva

Numerade Educator

01:04

Problem 6

Solve each equation. Check each solution.
$$
-8=8+z
$$

Julie Silva

Numerade Educator

01:15

Problem 7

Solve each equation. Check each solution.
$$
r-8.6=-8.1
$$

Julie Silva

Numerade Educator

01:09

Problem 8

Solve each equation. Check each solution.
$$
t-9.2=-6.8
$$

Julie Silva

Numerade Educator

01:03

Problem 9

Solve each equation. Check each solution.
$$
x-\frac{2}{5}=-\frac{3}{20}
$$

Julie Silva

Numerade Educator

01:00

Problem 10

Solve each equation. Check each solution.
$$
y-\frac{4}{7}=-\frac{3}{14}
$$

Julie Silva

Numerade Educator

01:03

Problem 11

Solve each equation. Check each solution.
$$
\frac{1}{3}+f=\frac{3}{4}
$$

Julie Silva

Numerade Educator

01:05

Problem 12

Solve each equation. Check each solution.
$$
c+\frac{1}{6}=\frac{3}{8}
$$

Julie Silva

Numerade Educator

00:47

Problem 13

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
7 x+2 x=8 x-3
$$

Julie Silva

Numerade Educator

00:51

Problem 14

$$
3 n+2 n=7+4 n
$$

Julie Silva

Numerade Educator

00:42

Problem 15

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{5}{6} x+\frac{1}{6} x=-9
$$

Julie Silva

Numerade Educator

00:44

Problem 16

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{13}{11} y-\frac{2}{11} y=-3
$$

Julie Silva

Numerade Educator

01:10

Problem 17

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
2 y+10=5 y-4 y
$$

Julie Silva

Numerade Educator

01:11

Problem 18

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
4 x-4=10 x-7 x
$$

Julie Silva

Numerade Educator

01:08

Problem 19

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-5(n-2)=8-4 n
$$

Julie Silva

Numerade Educator

01:12

Problem 20

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-4(z-3)=2-3 z
$$

Julie Silva

Numerade Educator

00:59

Problem 21

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{3}{7} x+2=-\frac{4}{7} x-5
$$

Julie Silva

Numerade Educator

01:00

Problem 22

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{1}{5} x-1=-\frac{4}{5} x-13
$$

Julie Silva

Numerade Educator

01:01

Problem 23

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
5 x-6=6 x-5
$$

Julie Silva

Numerade Educator

01:04

Problem 24

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
2 x+7=x-10
$$

Julie Silva

Numerade Educator

01:16

Problem 25

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
8 y+2-6 y=3+y-10
$$

Julie Silva

Numerade Educator

01:16

Problem 26

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
4 p-11-p=2+2 p-20
$$

Julie Silva

Numerade Educator

01:08

Problem 27

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-3(x-4)=-4 x
$$

Julie Silva

Numerade Educator

01:07

Problem 28

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-2(x-1)=-3 x
$$

Julie Silva

Numerade Educator

01:17

Problem 29

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{3}{8} x-\frac{1}{6}=-\frac{5}{8} x-\frac{2}{3}
$$

Julie Silva

Numerade Educator

01:16

Problem 30

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
\frac{2}{5} x-\frac{1}{12}=-\frac{3}{5} x-\frac{3}{4}
$$

Julie Silva

Numerade Educator

00:58

Problem 31

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
2(x-4)=x+3
$$

Julie Silva

Numerade Educator

01:08

Problem 32

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
3(y+7)=2 y-5
$$

Julie Silva

Numerade Educator

01:28

Problem 33

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
3(n-5)-(6-2 n)=4 n
$$

Julie Silva

Numerade Educator

01:32

Problem 34

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
5(3+z)-(8 z+9)=-4 z
$$

Julie Silva

Numerade Educator

01:41

Problem 35

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-2(x+6)+3(2 x-5)=3(x-4)+10
$$

Julie Silva

Numerade Educator

01:43

Problem 36

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 .
$$
-5(x+1)+4(2 x-3)=2(x+2)-8
$$

Julie Silva

Numerade Educator

00:41

Problem 37

Solve.
$$
13 x-3=14 x
$$

Julie Silva

Numerade Educator

00:40

Problem 38

Solve.
$$
18 x-9=19 x
$$

Julie Silva

Numerade Educator

00:44

Problem 39

Solve.
$$
5 b-0.7=6 b
$$

Julie Silva

Numerade Educator

00:42

Problem 40

Solve.
$$
9 x+5.5=10 x
$$

Julie Silva

Numerade Educator

00:56

Problem 41

Solve.
$$
3 x-6=2 x+5
$$

Julie Silva

Numerade Educator

00:58

Problem 42

Solve.
$$
7 y+2=6 y+2
$$

Julie Silva

Numerade Educator

01:18

Problem 43

Solve.
$$
13 x-9+2 x-5=12 x-1+2 x
$$

Julie Silva

Numerade Educator

01:18

Problem 44

Solve.
$$
15 x+20-10 x-9=25 x+8-21 x-7
$$

Julie Silva

Numerade Educator

01:18

Problem 45

Solve.
$$
7(6+w)=6(2+w)
$$

Julie Silva

Numerade Educator

01:17

Problem 46

Solve.
$$
6(5+c)=5(c-4)
$$

Julie Silva

Numerade Educator

00:44

Problem 47

Solve.
$$
n+4=3.6
$$

Julie Silva

Numerade Educator

00:45

Problem 48

Solve.
$$
m+2=7.1
$$

Julie Silva

Numerade Educator

01:31

Problem 49

Solve.
$$
10-(2 x-4)=7-3 x
$$

Julie Silva

Numerade Educator

01:21

Problem 50

Solve.
$$
15-(6-7 k)=2+6 k
$$

Julie Silva

Numerade Educator

00:45

Problem 51

Solve.
$$
\frac{1}{3}=x+\frac{2}{3}
$$

Julie Silva

Numerade Educator

00:51

Problem 52

Solve.
$$
\frac{1}{11}=y+\frac{10}{11}
$$

Julie Silva

Numerade Educator

01:29

Problem 53

Solve.
$$
-6.5-4 x-1.6-3 x=-6 x+9.8
$$

Julie Silva

Numerade Educator

01:18

Problem 54

Solve.
$$
-1.4-7 x-3.6-2 x=-8 x+4.4
$$

Julie Silva

Numerade Educator

01:20

Problem 55

Write each algebraic expression described.
A 10 -foot board is cut into two pieces. If one piece is $x$ feet long, express the other length in terms of $x$.

Julie Silva

Numerade Educator

00:53

Problem 56

Write each algebraic expression described.
A 5 -foot piece of string is cut into two pieces. If one piece is $x$ feet long, express the other length in terms of $x$.

Julie Silva

Numerade Educator

00:31

Write each algebraic expression described.
Recall that two angles are supplementary if their sum is $180^{\circ} .$ If one angle measures $x^{\circ},$ express the measure of its supplement in terms of $x$.

Julie Silva

Numerade Educator

00:36

Problem 58

Write each algebraic expression described.
Recall that two angles are complementary if their sum is $90^{\circ} .$ If one angle measures $x^{\circ},$ express the measure of its complement in terms of $x$.

Julie Silva

Numerade Educator

00:48

Problem 59

Write each algebraic expression described.
In $2009,$ the number of graduate students at the University of Texas at Austin was approximately 28,000 fewer than the number of undergraduate students. If the number of undergraduate students was $n$, how many graduate students attend UT Austin? (Source: University of Texas at Austin)

Julie Silva

Numerade Educator

01:19

Problem 60

Write each algebraic expression described.
The longest interstate highway in the U.S. is I-90, which connects Seattle, Washington, and Boston, Massachusetts. The second longest interstate highway, I- 80 (connecting San Francisco, California, and Teaneck, New Jersey), is 178.5 miles shorter than I-90. If the length of I- 80 is $m$ miles, express the length of I-90 as an algebraic expression in $m$. (Source: U.S. Department of TransportationFederal Highway Administration)

Julie Silva

Numerade Educator

00:47

Problem 61

Write each algebraic expression described.
The area of the Sahara Desert in Africa is 7 times the area of the Gobi Desert in Asia. If the area of the Gobi Desert is $x$ square miles, express the area of the Sahara Desert as an algebraic expression in $x$.

Julie Silva

Numerade Educator

00:51

Problem 62

Write each algebraic expression described.
The largest meteorite in the world is the Hoba West located in Namibia. Its weight is 3 times the weight of the Armanty meteorite located in Outer Mongolia. If the weight of the Armanty meteorite is $y$ kilograms, express the weight of the Hoba West meteorite as an algebraic expression in $y$.

Julie Silva

Numerade Educator

00:43

Problem 63

Find each multiplicative inverse or reciprocal.
$$
\frac{5}{8}
$$

Julie Silva

Numerade Educator

00:39

Problem 64

Find each multiplicative inverse or reciprocal.
$$
\frac{7}{6}
$$

Julie Silva

Numerade Educator

00:38

Problem 65

Find each multiplicative inverse or reciprocal.
$$
2
$$

Julie Silva

Numerade Educator

00:45

Problem 66

Find each multiplicative inverse or reciprocal.
$$
5
$$

Julie Silva

Numerade Educator

00:56

Problem 67

Find each multiplicative inverse or reciprocal.
$$
-\frac{1}{9}
$$

Julie Silva

Numerade Educator

00:54

Problem 68

Find each multiplicative inverse or reciprocal.
$$
-\frac{3}{5}
$$

Julie Silva

Numerade Educator

00:40

Problem 69

Perform each indicated operation and simplify.
$$
\frac{3 x}{3}
$$

Julie Silva

Numerade Educator

00:46

Problem 70

Perform each indicated operation and simplify.
$$
\frac{-2 y}{-2}
$$

Julie Silva

Numerade Educator

01:02

Problem 71

Perform each indicated operation and simplify.
$$
-5\left(-\frac{1}{5} y\right)
$$

Julie Silva

Numerade Educator

00:59

Problem 72

Perform each indicated operation and simplify.
$$
7\left(\frac{1}{7} r\right)
$$

Julie Silva

Numerade Educator

01:01

Problem 73

Perform each indicated operation and simplify.
$$
\frac{3}{5}\left(\frac{5}{3} x\right)
$$

Julie Silva

Numerade Educator

01:00

Problem 74

Perform each indicated operation and simplify.
$$
\frac{9}{2}\left(\frac{2}{9} x\right)
$$

Julie Silva

Numerade Educator

00:28

Problem 75

Write two terms whose sum is $-3 x$.

Ian Maurer

Numerade Educator

00:36

Problem 76

Write four terms whose sum is $2 y-6$.

Ian Maurer

Numerade Educator

00:35

Problem 77

Use the addition property to fill in the blank so that the middle equation simplifies to the last equation. See the Concept Check in this section.
$$
\begin{aligned}
x-4 &=-9 \\
x-4+(\quad) &=-9+(\quad) \\
x &=-5
\end{aligned}
$$

Ian Maurer

Numerade Educator

00:39

Problem 78

Use the addition property to fill in the blank so that the middle equation simplifies to the last equation. See the Concept Check in this section.
$$
\begin{aligned}
a+9 &=15 \\
a+9+(\quad) &=15+(\quad) \\
a &=6
\end{aligned}
$$

Ian Maurer

Numerade Educator

00:35

Problem 79

Fill in the blanks with numbers of your choice so that each equation has the given solution. Note: Each blank will be replaced with a different number.
__________ $+x=$ ___________ ;Solution: -3

Ian Maurer

Numerade Educator

00:32

Problem 80

Fill in the blanks with numbers of your choice so that each equation has the given solution. Note: Each blank will be replaced with a different number.
$x-$ ________ $=$ _______; Solution: -10

Ian Maurer

Numerade Educator

01:14

Problem 81

The sum of the angles of a triangle is $180^{\circ} .$ If one angle of a triangle measures $x^{\circ}$ and a second angle measures $(2 x+7)^{\circ},$ express the measure of the third angle in terms of $x$. Simplify the expression.

Ian Maurer

Numerade Educator

01:07

Problem 82

A quadrilateral is a four-sided figure (like the one shown in the figure) whose angle sum is $360^{\circ} .$ If one angle measures $x^{\circ},$ a second angle measures $3 x^{\circ},$ and a third angle measures $5 x^{\circ},$ express the measure of the fourth angle in terms of $x$. Simplify the expression.

Julie Silva

Numerade Educator

01:07

Problem 83

In your own words, explain what is meant by the solution of an equation.

Julie Silva

Numerade Educator

01:14

Problem 84

In your own words, explain how to check a solution of an equation.

Julie Silva

Numerade Educator

01:05

Problem 85

Use a calculator to determine the solution of each equation.
$$
36.766+x=-108.712
$$

Julie Silva

Numerade Educator

01:09

Problem 86

Use a calculator to determine the solution of each equation.
$$
\text { Use a calculator to determine the solution of each equation. }
$$

Julie Silva

Numerade Educator

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Problem 51

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