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.
14x−12=−34
34x−12=14
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x=1
56y−23=−32
56y−13=−76
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y=−1
12a+38=34
58b+12=−34
- Answer
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b=−2
2=13x−12x+23x
2=35x−13x+25x
- Answer
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x=3
14m−45m+12m=−1
56n−14n−12n=−2
- Answer
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n=−24
x+12=23x−12
x+34=12x−54
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x=−4
13w+54=w−14
32z+13=z−23
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z=−2
12x−14=112x+16
12a−14=16a+112
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a=1
13b+15=25b−35
13x+25=15x−25
- Answer
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x=−6
1=16(12x−6)
1=15(15x−10)
- Answer
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x=1
14(p−7)=13(p+5)
15(q+3)=12(q−3)
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q=7
12(x+4)=34
13(x+5)=56
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x=−52
5q−85=2q10
4m+26=m3
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m=−1
4n+84=n3
3p+63=p2
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p=−4
u3−4=u2−3
v10+1=v4−2
- Answer
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v=20
c15+1=c10−1
d6+3=d8+2
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d=−24
3x+42+1=5x+108
10y−23+3=10y+19
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y=−1
7u−14−1=4u+85
3v−62+5=11v−45
- Answer
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v=4
Solve Equations with Decimal Coefficients
In the following exercises, solve each equation with decimal coefficients.
0.6y+3=9
0.4y−4=2
- Answer
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y=15
3.6j−2=5.2
2.1k+3=7.2
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k=2
0.4x+0.6=0.5x−1.2
0.7x+0.4=0.6x+2.4
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x=20
0.23x+1.47=0.37x−1.05
0.48x+1.56=0.58x−0.64
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x=22
0.9x−1.25=0.75x+1.75
1.2x−0.91=0.8x+2.29
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x=8
0.05n+0.10(n+8)=2.15
0.05n+0.10(n+7)=3.55
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n=19
0.10d+0.25(d+5)=4.05
0.10d+0.25(d+7)=5.25
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d=10
0.05(q−5)+0.25q=3.05
0.05(q−8)+0.25q=4.10
- Answer
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q=15
Everyday Math
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.
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(s−8)=22.82 for s, to find the number of 49-cent stamps Paula bought.
- Answer
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s=35
Writing Exercises
Explain how you find the least common denominator of 38,16, and 23
If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?
- Answer
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Answers will vary.
If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?
In the equation 0.35x+2.1=3.85 what is the LCD? How do you know?
- Answer
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100. Justifications will vary.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?