# 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. $9x-3=60$

2. $12x-8=64$

Solution

$x=6$

3. $14w+5=117$

4. $15y+7=97$

Solution

$y=6$

5. $2a+8=-28$

6. $3m+9=-15$

Solution

$m=-8$

7. $-62=8n-6$

8. $-77=9b-5$

Solution

$b=-8$

9. $35=-13y+9$

10. $60=-21x-24$

Solution

$x=-4$

11. $-12p-9=9$

12. $-14q-2=16$

Solution

$q=-\frac{9}{7}$

## Exercises: Solve Equations with Variables on Both Sides

Instructions: For questions 13-24, solve the following equations with variables on both sides.

13. $19z=18z-7$

14. $21k=20k-11$

Solution

$k=-11$

15. $9x+36=15x$

16. $8x+27=11x$

Solution

$x=9$

17. $c=-3c-20$

18. $b=-4b-15$

Solution

$b=-3$

19. $9q=44-2q$

20. $5z=39-8z$

Solution

$z=3$

21. $6y+\frac{1}{2}=5y$

22. $4x+\frac{3}{4}=3x$

Solution

$x=-\frac{3}{4}$

23. $-18a-8=-22a$

24. $-11r-8=-7r$

Solution

$r=-2$

## 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. $8x-15=7x+3$

26. $6x-17=5x+2$

Solution

$x=19$

27. $26+13d=14d+11$

28. $21+18f=19f+14$

Solution

$f=7$

29. $2p-1=4p-33$

30. $12q-5=9q-20$

Solution

$q=-5$

31. $4a+5=-a-40$

32. $8c+7=-3c-37$

Solution

$c=-4$

33. $5y-30=-5y+30$

34. $7x-17=-8x+13$

Solution

$x=2$

35. $7s+12=5+4s$

36. $9p+14=6+4p$

Solution

$p=-\frac{8}{5}$

37. $2z-6=23-z$

38. $3y-4=12-y$

Solution

$y=4$

39. $\frac{5}{3}c-3=\frac{2}{3}c-16$

40. $\frac{7}{4}m-7=\frac{3}{4}m-13$

Solution

$m=-6$

41. $8-\frac{2}{5}q=\frac{3}{5}q+6$

42. $11-\frac{1}{5}a=\frac{4}{5}a+4$

Solution

$a=7$

43. $\frac{4}{3}n+9=\frac{1}{3}n-9$

44. $\frac{5}{4}a+15=\frac{3}{4}a-5$

Solution

$a=-40$

45. $\frac{1}{4}y+7=\frac{3}{4}y-3$

46. $\frac{3}{5}p+2=\frac{4}{5}p-1$

Solution

$p=15$

47. $14n+8.25=9n+19.60$

48. $13z+6.45=8z+23.75$

Solution

$z=3.46$

49. $2.4w-100=0.8w+28$

50. $2.7w-80=1.2w+10$

Solution

$w=60$

51. $5.6r+13.1=3.5r+57.2$

52. $6.6x-18.9=3.4x+54.7$

Solution

$x=23$

## 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 $1506$. Student tickets sold for $6$ and adult tickets sold for $9$. The number of adult tickets sold was 5 less than 3 times the number of student tickets. Find the number of student tickets sold, $s$, by solving the equation $6s+27s-45=1506$.

54. Making a fence. Jovani has $150$ feet of fencing to make a rectangular garden in his backyard. He wants the length to be $15$ feet more than the width. Find the width, $w$, by solving the equation $150=2w+30+2w$.

Solution

$30$ feet

## Exercises: Writing Exercises

Instructions: For questions 55-58, answer the given writing exercises.

55. Solve the equation $\frac{6}{5}y-8=\frac{1}{5}y+7$ explaining all the steps of your solution as in the examples in this section.

56. Solve the equation $10x+14=-2x+38$ explaining all the steps of your solution as in the examples in this section.

Solution

$x=2$ (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 $x$ to be the “variable” side?

58. Is $x=-2$ a solution to the equation $5-2x=-4x+1$ ? How do you know?

Solution

Yes. Justifications will vary.