Exercises: Solve Equations with Fractions or Decimals (3.5)
Exercises: Solve Equations with Fraction Coefficients
Instructions: For questions 1-36, solve each equation with fraction coefficients.
1. [latex]\frac{1}{4}x-\frac{1}{2}=-\frac{3}{4}[/latex]
2. [latex]\frac{3}{4}x-\frac{1}{2}=\frac{1}{4}[/latex]
Solution
[latex]x=1[/latex]
3. [latex]\frac{5}{6}y-\frac{2}{3}=-\frac{3}{2}[/latex]
4. [latex]\frac{5}{6}y-\frac{1}{3}=-\frac{7}{6}[/latex]
Solution
[latex]y=-1[/latex]
5. [latex]\frac{1}{2}a+\frac{3}{8}=\frac{3}{4}[/latex]
6. [latex]\frac{5}{8}b+\frac{1}{2}=-\frac{3}{4}[/latex]
Solution
[latex]b=-2[/latex]
7. [latex]2=\frac{1}{3}x-\frac{1}{2}x+\frac{2}{3}x[/latex]
8. [latex]2=\frac{3}{5}x-\frac{1}{3}x+\frac{2}{5}x[/latex]
Solution
[latex]x=3[/latex]
9. [latex]\frac{1}{4}m-\frac{4}{5}m+\frac{1}{2}m=-1[/latex]
10. [latex]\frac{5}{6}n-\frac{1}{4}n-\frac{1}{2}n=-2[/latex]
Solution
[latex]n=-24[/latex]
11. [latex]x+\frac{1}{2}=\frac{2}{3}x-\frac{1}{2}[/latex]
12. [latex]x+\frac{3}{4}=\frac{1}{2}x-\frac{5}{4}[/latex]
Solution
[latex]x=-4[/latex]
13. [latex]\frac{1}{3}w+\frac{5}{4}=w-\frac{1}{4}[/latex]
14. [latex]\frac{3}{2}z+\frac{1}{3}=z-\frac{2}{3}[/latex]
Solution
[latex]z=-2[/latex]
15. [latex]\frac{1}{2}x-\frac{1}{4}=\frac{1}{12}x+\frac{1}{6}[/latex]
16. [latex]\frac{1}{2}a-\frac{1}{4}=\frac{1}{6}a+\frac{1}{12}[/latex]
Solution
[latex]a=1[/latex]
17. [latex]\frac{1}{3}b+\frac{1}{5}=\frac{2}{5}b-\frac{3}{5}[/latex]
18. [latex]\frac{1}{3}x+\frac{2}{5}=\frac{1}{5}x-\frac{2}{5}[/latex]
Solution
[latex]x=-6[/latex]
19. [latex]1=\frac{1}{6}(12x-6)[/latex]
20. [latex]1=\frac{1}{5}(15x-10)[/latex]
Solution
[latex]x=1[/latex]
21. [latex]\frac{1}{4}\left(p-7\right)=\frac{1}{3}\left(p+5\right)[/latex]
22. [latex]\frac{1}{5}(q+3)=\frac{1}{2}(q-3)[/latex]
Solution
[latex]q=7[/latex]
23. [latex]\frac{1}{2}(x+4)=\frac{3}{4}[/latex]
24. [latex]\frac{1}{3}(x+5)=\frac{5}{6}[/latex]
Solution
[latex]x=-\frac{5}{2}[/latex]
25. [latex]\frac{5q-8}{5}=\frac{2q}{10}[/latex]
26. [latex]\frac{4m+2}{6}=\frac{m}{3}[/latex]
Solution
[latex]m=-1[/latex]
27. [latex]\frac{4n+8}{4}=\frac{n}{3}[/latex]
28. [latex]\frac{3p+6}{3}=\frac{p}{2}[/latex]
Solution
[latex]p=-4[/latex]
29. [latex]\frac{u}{3}-4=\frac{u}{2}-3[/latex]
30. [latex]\frac{v}{10}+1=\frac{v}{4}-2[/latex]
Solution
[latex]v=20[/latex]
31. [latex]\frac{c}{15}+1=\frac{c}{10}-1[/latex]
32. [latex]\frac{d}{6}+3=\frac{d}{8}+2[/latex]
Solution
[latex]d=-24[/latex]
33. [latex]\frac{3x+4}{2}+1=\frac{5x+10}{8}[/latex]
34. [latex]\frac{10y-2}{3}+3=\frac{10y+1}{9}[/latex]
Solution
[latex]y=-1[/latex]
35. [latex]\frac{7u-1}{4}-1=\frac{4u+8}{5}[/latex]
36. [latex]\frac{3v-6}{2}+5=\frac{11v-4}{5}[/latex]
Solution
[latex]v=4[/latex]
Exercises: Solve Equations with Decimal Coefficients
Instructions: For questions 37-52, solve each equation with decimal coefficients.
37. [latex]0.6y+3=9[/latex]
38. [latex]0.4y-4=2[/latex]
Solution
[latex]y=15[/latex]
39. [latex]3.6j-2=5.2[/latex]
40. [latex]2.1k+3=7.2[/latex]
Solution
[latex]k=2[/latex]
41. [latex]0.4x+0.6=0.5x-1.2[/latex]
42. [latex]0.7x+0.4=0.6x+2.4[/latex]
Solution
[latex]x=20[/latex]
43. [latex]0.23x+1.47=0.37x-1.05[/latex]
44. [latex]0.48x+1.56=0.58x-0.64[/latex]
Solution
[latex]x=22[/latex]
45. [latex]0.9x-1.25=0.75x+1.75[/latex]
46. [latex]1.2x-0.91=0.8x+2.29[/latex]
Solution
[latex]x=8[/latex]
47. [latex]0.05n+0.10(n+8)=2.15[/latex]
48. [latex]0.05n+0.10(n+7)=3.55[/latex]
Solution
[latex]n=19[/latex]
49. [latex]0.10d+0.25(d+5)=4.05[/latex]
50. [latex]0.10d+0.25(d+7)=5.25[/latex]
Solution
[latex]d=10[/latex]
51. [latex]0.05(q-5)+0.25q=3.05[/latex]
52. [latex]0.05(q-8)+0.25q=4.10[/latex]
Solution
[latex]q=15[/latex]
Exercises: Everyday Math
Instructions: For questions 53-54, answer the given everyday math word problems.
53. Coins.Taylor has [latex]$2.00[/latex] in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation [latex]0.10d+0.01(d+2)=2[/latex] for [latex]d[/latex], the number of dimes.
54. Stamps.Paula bought [latex]$22.82[/latex] 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 [latex]0.49s+0.21\left(s-8\right)=22.82[/latex] for [latex]s[/latex], to find the number of 49-cent stamps Paula bought.
Solution
[latex]s=35[/latex]
Exercises: Writing Exercises
Instructions: For questions 55-58, answer the given writing exercises.
55. Explain how you find the least common denominator of [latex]\frac{3}{8}[/latex], [latex]\frac{1}{6}[/latex], and [latex]\frac{2}{3}[/latex].
56. If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?
Solution
Answers will vary.
57. If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?
58. In the equation [latex]0.35x+2.1=3.85[/latex] what is the LCD? How do you know?
Solution
100. Justifications will vary.
