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Mathematics LibreTexts

2.5E: Exercises

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Practice Makes Perfect

Solve Equations with Fraction Coefficients

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

Exercise 2.5E.1

14x12=34

Exercise 2.5E.2

34x12=14

Answer

x=1

Exercise 2.5E.3

56y23=32

Exercise 2.5E.4

56y13=76

Answer

y=1

Exercise 2.5E.5

12a+38=34

Exercise 2.5E.6

58b+12=34

Answer

b=2

Exercise 2.5E.7

2=13x12x+23x

Exercise 2.5E.8

2=35x13x+25x

Answer

x=3

Exercise 2.5E.9

14m45m+12m=1

Exercise 2.5E.10

56n14n12n=2

Answer

n=24

Exercise 2.5E.11

x+12=23x12

Exercise 2.5E.12

x+34=12x54

Answer

x=4

Exercise 2.5E.13

13w+54=w14

Exercise 2.5E.14

32z+13=z23

Answer

z=2

Exercise 2.5E.15

12x14=112x+16

Exercise 2.5E.16

12a14=16a+112

Answer

a=1

Exercise 2.5E.17

13b+15=25b35

Exercise 2.5E.18

13x+25=15x25

Answer

x=6

Exercise 2.5E.19

1=16(12x6)

Exercise 2.5E.20

1=15(15x10)

Answer

x=1

Exercise 2.5E.21

14(p7)=13(p+5)

Exercise 2.5E.22

15(q+3)=12(q3)

Answer

q=7

Exercise 2.5E.23

12(x+4)=34

Exercise 2.5E.24

13(x+5)=56

Answer

x=52

Exercise 2.5E.25

5q85=2q10

Exercise 2.5E.26

4m+26=m3

Answer

m=1

Exercise 2.5E.27

4n+84=n3

Exercise 2.5E.28

3p+63=p2

Answer

p=4

Exercise 2.5E.29

u34=u23

Exercise 2.5E.30

v10+1=v42

Answer

v=20

Exercise 2.5E.31

c15+1=c101

Exercise 2.5E.32

d6+3=d8+2

Answer

d=24

Exercise 2.5E.33

3x+42+1=5x+108

Exercise 2.5E.34

10y23+3=10y+19

Answer

y=1

Exercise 2.5E.35

7u141=4u+85

Exercise 2.5E.36

3v62+5=11v45

Answer

v=4

Solve Equations with Decimal Coefficients

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

Exercise 2.5E.37

0.6y+3=9

Exercise 2.5E.38

0.4y4=2

Answer

y=15

Exercise 2.5E.39

3.6j2=5.2

Exercise 2.5E.40

2.1k+3=7.2

Answer

k=2

Exercise 2.5E.41

0.4x+0.6=0.5x1.2

Exercise 2.5E.42

0.7x+0.4=0.6x+2.4

Answer

x=20

Exercise 2.5E.43

0.23x+1.47=0.37x1.05

Exercise 2.5E.44

0.48x+1.56=0.58x0.64

Answer

x=22

Exercise 2.5E.45

0.9x1.25=0.75x+1.75

Exercise 2.5E.46

1.2x0.91=0.8x+2.29

Answer

x=8

Exercise 2.5E.47

0.05n+0.10(n+8)=2.15

Exercise 2.5E.48

0.05n+0.10(n+7)=3.55

Answer

n=19

Exercise 2.5E.49

0.10d+0.25(d+5)=4.05

Exercise 2.5E.50

0.10d+0.25(d+7)=5.25

Answer

d=10

Exercise 2.5E.51

0.05(q5)+0.25q=3.05

Exercise 2.5E.52

0.05(q8)+0.25q=4.10

Answer

q=15

Everyday Math

Exercise 2.5E.53

Coins Taylor has $200 in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation 0.10d+0.01(d+2)=2 for d, the number of dimes.

Exercise 2.5E.54

Stamps Paula bought $22.82 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 8 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s8)=22.82 for s, to find the number of 49-cent stamps Paula bought.

Answer

s=35

Writing Exercises

Exercise 2.5E.55

Explain how you find the least common denominator of 38,16, and 23

Exercise 2.5E.56

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?

Answer

Answers will vary.

Exercise 2.5E.57

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

Exercise 2.5E.58

In the equation 0.35x+2.1=3.85 what is the LCD? How do you know?

Answer

100. Justifications will vary.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads: “solve equations with fraction coefficients,” and “solve equations with decimal coefficients.” The rest of the cells are blank.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?


This page titled 2.5E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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