Key Terms

Solve Equations using the Subtraction and Addition Properties of Equality

Verify a Solution of an Equation

In the following exercises, determine whether each number is a solution to the equation.512

10x−1=5x;x=1510x−1=5x;x=15513

w+2=58;w=38w+2=58;w=38514

−12n+5=8n;n=−54−12n+5=8n;n=−54515

6a−3=−7a,a=3136a−3=−7a,a=313

Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, solve each equation using the Subtraction Property of Equality.516

x+7=19x+7=19517

y+2=−6y+2=−6518

a+13=53a+13=53519

n+3.6=5.1n+3.6=5.1

In the following exercises, solve each equation using the Addition Property of Equality.520

u−7=10u−7=10521

x−9=−4x−9=−4522

c−311=911c−311=911523

p−4.8=14p−4.8=14

In the following exercises, solve each equation.524

n−12=32n−12=32525

y+16=−9y+16=−9526

f+23=4f+23=4527

d−3.9=8.2d−3.9=8.2

Solve Equations That Require Simplification

In the following exercises, solve each equation.528

y+8−15=−3y+8−15=−3529

7x+10−6x+3=57x+10−6x+3=5530

6(n−1)−5n=−146(n−1)−5n=−14531

8(3p+5)−23(p−1)=358(3p+5)−23(p−1)=35

Translate to an Equation and Solve

In the following exercises, translate each English sentence into an algebraic equation and then solve it.532

The sum of −6−6 and mm is 25.533

Four less than nn is 13.

Translate and Solve Applications

In the following exercises, translate into an algebraic equation and solve.534

Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son?535

Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?536

Peter paid $9.75 to go to the movies, which was $46.25 less than he paid to go to a concert. How much did he pay for the concert?537

Elissa earned $152.84 this week, which was $21.65 more than she earned last week. How much did she earn last week?

Solve Equations using the Division and Multiplication Properties of Equality

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.538

8x=728x=72539

13a=−6513a=−65540

0.25p=5.250.25p=5.25541

−y=4−y=4542

n6=18n6=18543

y−10=30y−10=30544

36=34×36=34x545

58u=151658u=1516546

−18m=−72−18m=−72547

c9=36c9=36548

0.45x=6.750.45x=6.75549

1112=23y1112=23y

Solve Equations That Require Simplification

In the following exercises, solve each equation requiring simplification.550

5r−3r+9r=35−25r−3r+9r=35−2551

24x+8x−11x=−7−1424x+8x−11x=−7−14552

1112n−56n=9−51112n−56n=9−5553

−9(d−2)−15=−24−9(d−2)−15=−24

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.554

143 is the product of −11−11 and y.555

The quotient of b and and 9 is −27−27.556

The sum of q and one-fourth is one.557

The difference of s and one-twelfth is one fourth.

Translate and Solve Applications

In the following exercises, translate into an equation and solve.558

Ray paid $21 for 12 tickets at the county fair. What was the price of each ticket?559

Janet gets paid $24 per hour. She heard that this is 3434 of what Adam is paid. How much is Adam paid per hour?

Solve Equations with Variables and Constants on Both Sides

Solve an Equation with Constants on Both Sides

In the following exercises, solve the following equations with constants on both sides.560

8p+7=478p+7=47561

10w−5=6510w−5=65562

3x+19=−473x+19=−47563

32=−4−9n32=−4−9n

Solve an Equation with Variables on Both Sides

In the following exercises, solve the following equations with variables on both sides.564

7y=6y−137y=6y−13565

5a+21=2a5a+21=2a566

k=−6k−35k=−6k−35567

4x−38=3x4x−38=3x

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the following equations with variables and constants on both sides.568

12x−9=3x+4512x−9=3x+45569

5n−20=−7n−805n−20=−7n−80570

4u+16=−19−u4u+16=−19−u571

58c−4=38c+458c−4=38c+4

Use a General Strategy for Solving Linear Equations

Solve Equations Using the General Strategy for Solving Linear Equations

In the following exercises, solve each linear equation.572

6(x+6)=246(x+6)=24573

9(2p−5)=729(2p−5)=72574

−(s+4)=18−(s+4)=18575

8+3(n−9)=178+3(n−9)=17576

23−3(y−7)=823−3(y−7)=8577

13(6m+21)=m−713(6m+21)=m−7578

4(3.5y+0.25)=3654(3.5y+0.25)=365579

0.25(q−8)=0.1(q+7)0.25(q−8)=0.1(q+7)580

8(r−2)=6(r+10)8(r−2)=6(r+10)581

5+7(2−5x)=2(9x+1)5+7(2−5x)=2(9x+1)
−(13x−57)−(13x−57)582

(9n+5)−(3n−7)(9n+5)−(3n−7)
=20−(4n−2)=20−(4n−2)583

2[−16+5(8k−6)]2[−16+5(8k−6)]
=8(3−4k)−32=8(3−4k)−32

Classify Equations

In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.584

17y−3(4−2y)=11(y−1)17y−3(4−2y)=11(y−1)
+12y−1+12y−1585

9u+32=15(u−4)9u+32=15(u−4)
−3(2u+21)−3(2u+21)586

−8(7m+4)=−6(8m+9)−8(7m+4)=−6(8m+9)587

21(c−1)−19(c+1)21(c−1)−19(c+1)
=2(c−20)=2(c−20)

Solve Equations with Fractions and Decimals

Solve Equations with Fraction Coefficients

In the following exercises, solve each equation with fraction coefficients.588

25n−110=71025n−110=710589

13x+15x=813x+15x=8590

34a−13=12a−5634a−13=12a−56591

12(k−3)=13(k+16)12(k−3)=13(k+16)592

3x−25=3x+483x−25=3x+48593

5y−13+4=−8y+465y−13+4=−8y+46

Solve Equations with Decimal Coefficients

In the following exercises, solve each equation with decimal coefficients.594

0.8x−0.3=0.7x+0.20.8x−0.3=0.7x+0.2595

0.36u+2.55=0.41u+6.80.36u+2.55=0.41u+6.8596

0.6p−1.9=0.78p+1.70.6p−1.9=0.78p+1.7597

0.7y+2.5=0.95y−9.250.7y+2.5=0.95y−9.25

Solve a Formula for a Specific Variable

Use the Distance, Rate, and Time Formula

In the following exercises, solve.598

Natalie drove for 712712 hours at 60 miles per hour. How much distance did she travel?599

Mallory is taking the bus from St. Louis to Chicago. The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour. How long will the bus ride be?600

Aaron’s friend drove him from Buffalo to Cleveland. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron’s friend driving?601

Link rode his bike at a steady rate of 15 miles per hour for 212212 hours. How much distance did he travel?

Solve a Formula for a Specific Variable

In the following exercises, solve.602

Use the formula. d=rtd=rt to solve for t
ⓐ when d=510d=510 and r=60r=60
ⓑ in general603

Use the formula. d=rtd=rt to solve for rr
ⓐ when when d=451d=451 and t=5.5t=5.5
ⓑ in general604

Use the formula A=12bhA=12bh to solve for bb
ⓐ when A=390A=390 and h=26h=26
ⓑ in general605

Use the formula A=12bhA=12bh to solve for hh
ⓐ when A=153A=153 and b=18b=18
ⓑ in general606

Use the formula I=PrtI=Prt to solve for the principal, P for
ⓐ I=$2,501,r=4.1%,I=$2,501,r=4.1%,
t=5yearst=5years
ⓑ in general607

Solve the formula 4x+3y=64x+3y=6 for y
ⓐ when x=−2x=−2
ⓑ in general608

Solve 180=a+b+c180=a+b+c for cc.609

Solve the formula V=LWHV=LWH for HH.

Solve Linear Inequalities

Graph Inequalities on the Number Line

In the following exercises, graph each inequality on the number line.610.


ⓐ x≤4x≤4
ⓑ x>−2x>−2
ⓒ x<1x<1611.


ⓐ x>0x>0
ⓑ x<−3x<−3
ⓒ x≥−1x≥−1

In the following exercises, graph each inequality on the number line and write in interval notation.612.


ⓐ x<−1x<−1
ⓑ x≥−2.5x≥−2.5
ⓒ x≤54x≤54613.


ⓐ x>2x>2
ⓑ x≤−1.5x≤−1.5
ⓒ x≥53x≥53

Solve Inequalities using the Subtraction and Addition Properties of Inequality

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.614

n−12≤23n−12≤23615

m+14≤56m+14≤56616

a+23≥712a+23≥712617

b−78≥−12b−78≥−12

Solve Inequalities using the Division and Multiplication Properties of Inequality

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.618

9x>549x>54619

−12d≤108−12d≤108620

56j<−6056j<−60621

q−2≥−24q−2≥−24

Solve Inequalities That Require Simplification

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.622

6p>15p−306p>15p−30623

9h−7(h−1)≤4h−239h−7(h−1)≤4h−23624

5n−15(4−n)<10(n−6)+10n5n−15(4−n)<10(n−6)+10n625

38a−112a>512a+3438a−112a>512a+34

Translate to an Inequality and Solve

In the following exercises, translate and solve. Then write the solution in interval notation and graph on the number line.626

Five more than z is at most 19.627

Three less than c is at least 360.628

Nine times n exceeds 42.629

Negative two times a is no more than 8.

Everyday Math

630

Describe how you have used two topics from this chapter in your life outside of your math class during the past month.