Exercises: Solve Equations with Variables and Constants on Both Sides (3.3)
Exercises: Solve Equations with Constants on Both Sides
Instructions: For questions 1-12, solve the following equations with constants on both sides.
1. [latex]9x-3=60[/latex]
2. [latex]12x-8=64[/latex]
Solution
[latex]x=6[/latex]
3. [latex]14w+5=117[/latex]
4. [latex]15y+7=97[/latex]
Solution
[latex]y=6[/latex]
5. [latex]2a+8=-28[/latex]
6. [latex]3m+9=-15[/latex]
Solution
[latex]m=-8[/latex]
7. [latex]-62=8n-6[/latex]
8. [latex]-77=9b-5[/latex]
Solution
[latex]b=-8[/latex]
9. [latex]35=-13y+9[/latex]
10. [latex]60=-21x-24[/latex]
Solution
[latex]x=-4[/latex]
11. [latex]-12p-9=9[/latex]
12. [latex]-14q-2=16[/latex]
Solution
[latex]q=-\frac{9}{7}[/latex]
Exercises: Solve Equations with Variables on Both Sides
Instructions: For questions 13-24, solve the following equations with variables on both sides.
13. [latex]19z=18z-7[/latex]
14. [latex]21k=20k-11[/latex]
Solution
[latex]k=-11[/latex]
15. [latex]9x+36=15x[/latex]
16. [latex]8x+27=11x[/latex]
Solution
[latex]x=9[/latex]
17. [latex]c=-3c-20[/latex]
18. [latex]b=-4b-15[/latex]
Solution
[latex]b=-3[/latex]
19. [latex]9q=44-2q[/latex]
20. [latex]5z=39-8z[/latex]
Solution
[latex]z=3[/latex]
21. [latex]6y+\frac{1}{2}=5y[/latex]
22. [latex]4x+\frac{3}{4}=3x[/latex]
Solution
[latex]x=-\frac{3}{4}[/latex]
23. [latex]-18a-8=-22a[/latex]
24. [latex]-11r-8=-7r[/latex]
Solution
[latex]r=-2[/latex]
Exercises: Solve Equations with Variables and Constants on Both Sides
Instructions: For questions 25-52, solve the equations with variables and constants on both sides.
25. [latex]8x-15=7x+3[/latex]
26. [latex]6x-17=5x+2[/latex]
Solution
[latex]x=19[/latex]
27. [latex]26+13d=14d+11[/latex]
28. [latex]21+18f=19f+14[/latex]
Solution
[latex]f=7[/latex]
29. [latex]2p-1=4p-33[/latex]
30. [latex]12q-5=9q-20[/latex]
Solution
[latex]q=-5[/latex]
31. [latex]4a+5=-a-40[/latex]
32. [latex]8c+7=-3c-37[/latex]
Solution
[latex]c=-4[/latex]
33. [latex]5y-30=-5y+30[/latex]
34. [latex]7x-17=-8x+13[/latex]
Solution
[latex]x=2[/latex]
35. [latex]7s+12=5+4s[/latex]
36. [latex]9p+14=6+4p[/latex]
Solution
[latex]p=-\frac{8}{5}[/latex]
37. [latex]2z-6=23-z[/latex]
38. [latex]3y-4=12-y[/latex]
Solution
[latex]y=4[/latex]
39. [latex]\frac{5}{3}c-3=\frac{2}{3}c-16[/latex]
40. [latex]\frac{7}{4}m-7=\frac{3}{4}m-13[/latex]
Solution
[latex]m=-6[/latex]
41. [latex]8-\frac{2}{5}q=\frac{3}{5}q+6[/latex]
42. [latex]11-\frac{1}{5}a=\frac{4}{5}a+4[/latex]
Solution
[latex]a=7[/latex]
43. [latex]\frac{4}{3}n+9=\frac{1}{3}n-9[/latex]
44. [latex]\frac{5}{4}a+15=\frac{3}{4}a-5[/latex]
Solution
[latex]a=-40[/latex]
45. [latex]\frac{1}{4}y+7=\frac{3}{4}y-3[/latex]
46. [latex]\frac{3}{5}p+2=\frac{4}{5}p-1[/latex]
Solution
[latex]p=15[/latex]
47. [latex]14n+8.25=9n+19.60[/latex]
48. [latex]13z+6.45=8z+23.75[/latex]
Solution
[latex]z=3.46[/latex]
49. [latex]2.4w-100=0.8w+28[/latex]
50. [latex]2.7w-80=1.2w+10[/latex]
Solution
[latex]w=60[/latex]
51. [latex]5.6r+13.1=3.5r+57.2[/latex]
52. [latex]6.6x-18.9=3.4x+54.7[/latex]
Solution
[latex]x=23[/latex]
Exercises: Everyday Math
Instructions: For questions 25-46, answer the given everyday math word problems.
53. Concert tickets. At a school concert the total value of tickets sold was [latex]$1506[/latex]. Student tickets sold for [latex]$6[/latex] and adult tickets sold for [latex]9[/latex]. The number of adult tickets sold was 5 less than 3 times the number of student tickets. Find the number of student tickets sold, [latex]s[/latex], by solving the equation [latex]6s+27s-45=1506[/latex].
54. Making a fence. Jovani has [latex]150[/latex] feet of fencing to make a rectangular garden in his backyard. He wants the length to be [latex]15[/latex] feet more than the width. Find the width, [latex]w[/latex], by solving the equation [latex]150=2w+30+2w[/latex].
Solution
[latex]30[/latex] feet
Exercises: Writing Exercises
Instructions: For questions 55-58, answer the given writing exercises.
55. Solve the equation [latex]\frac{6}{5}y-8=\frac{1}{5}y+7[/latex] explaining all the steps of your solution as in the examples in this section.
56. Solve the equation [latex]10x+14=-2x+38[/latex] explaining all the steps of your solution as in the examples in this section.
Solution
[latex]x=2[/latex] (Justifications will vary.)
57. When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient of [latex]x[/latex] to be the “variable” side?
58. Is [latex]x=-2[/latex] a solution to the equation [latex]5-2x=-4x+1[/latex] ? How do you know?
Solution
Yes. Justifications will vary.
