MATH MODELS
LESSON 2.3
EQUATIONS WITH VARIABLES IN BOTH MEMBERS
Solve each equation below. Be sure to check your work on the calculator.
1. 3x = x – 9
2. 5x = 7x – 12
3. 4y = -3y + 21
4. -5y = 4y – 27
5. 8k + 16 = 4k
6. -4k – 22 = 7k
7. 3y + 7 = y + 13
8. 26 + 4k = 2k + 1
9. -9x + 35 = 4x + 9
10. x + 72 = 5x + 42
11. -4y + 19 = 27
12. 21 + 3w = 16.5
13. x – 9 = 4x + 12
14. 57 – 13x = 20x + 22
15. x + 23 = 10x + .5
16. 3.2x – 17 = 2.4x – 1
17. 4.7y – 8.2 = 8.3 – .8y
18. 3x – 47 = 10 – 2x
19. -3(2x + 4) = 4x + 18
20. 6(2y – 1) = 2y + 13
21. 8(3x – 4) = 4(4x + 2)
22. – (x – 5) = 3(x + 3)
23. 3x – 8 = 7x + 4
24. 12 – 3a = 5a – 4
25. 16 – x = x – 5
26. 1.2z – .8 = .7z – 2.3
27.
5 x 9 3x 5
 

6 16 4 8
29. 12 + 5c = 4c + 12
28. – 8x + 20 = -5x – 4
30. 16 – 4x = 4x – 4
31. 17 + 6x = 21 – 4x
32. 11 – 7x = 19 – 9x
33. 5x + 22 = 9x + 6
34. 18 – 3y = y – 12
35. 3.6 – .7x = .24 – x
36. 36 – 21y = 10 – 8y
37. p + 1.75 = .25p – 1.25
38. – x + 19 – x = 16 + 5x – 9
39. -18 + 4x + 7 = -3x + 6 – 6 x
40. 16 – x = 23 + x
41. – 9 – 6x = 21 – 10x
42. 31 + 3x = 5x + 31
43. – 5x + 23 – 6x = 6x – 11
44. 3(2x – 4) = 5(2x + 4)
45. – (7x – 13) = 3(x + 8)
46. -4 (9 – 3x) = -5(4 + 5x) – 16
47. .5(1.5x + 2.5) = .4(2.5x – 3 .5) – .1
48.
3
7
(15 x  30)  (56 x  24)  17
5
8
49. – (7x – 12) + 3x = 6(x – 4)
50. -4(2y – 3) + 5y = 3y – 5(y + 5)
51. 60     36     2
 12 15 
 9 3
5x
7
4x
2
52. – x + 3(6 – x) = - 6(x + 3) – 8
53. 9 + 7(x – 2) = 10x + 6(x – 4) – 7
54. 5(3x – 9 ) – 7x = 12x – 3(7x + 9)
55. .7(3x – 4) + 5 = .5(3x – 1.2 ) - .2
56. 6(3x – 7) = 18 – 3 (5x + 1) + 6
57. 9(4y – 7) + 27 = 3(4y – 1 ) – 11
Michael and Stan entered a jellybean eating contest at the high school. Stan
ate jellybeans at the rate of 24 per minute. Michael entered the contest two
minutes after Stan had entered, and he ate jellybeans at the rate of 28 per
minute. Let s represent the number of minutes Stan has been in the contest.
58. a. Define the variable.
b. Write an expression in terms of s that represents the number of
jellybeans Stan has eaten since he entered the contest.
c. Write an expression in terms of s that represents the number of
minutes Michael has been entered in the contest. Then write an
expression that represents the number of jellybeans Michael has
eaten .
d. How many jellybeans has Stan eaten after he has been in the contest
15 minutes?
e. How long has Stan been in the contest when he has eaten 132
jellybeans?
f. How many jellybeans has Michael eaten when Stan has been eating
for 8 minutes?
g. How long has Stan been eating when Michael has eaten 196
jellybeans?
h. How many minutes has Stan been entered in the contest when he
and Michael together have eaten a total of 360 jellybeans?
i. In which of problems a-h did you solve an equation?
j. Write the equation that indicates that Stan and Michael have
both consumed the same number of jellybeans.
k. How long did it take Michael to catch up to Stan in the contest?
l. What was the total number of jellybeans eaten by the boys at the
point in time when they had eaten equal numbers of jellybeans?
Dina and Julie are both taking a homemaking class. Today, their homemaking
class hosted a luncheon for the senior class. Dina an Julie have bben given the
task of washing all the dishes. Dina starts washing the dishes and five minutes
later she is joined by Julie. Dina washes dishes at the rate of 8 per minute and
Julie washes dishes at the rate of 10 per minute. Let d represent the number of
minutes that Dina has been washing dishes.
59. a. Define the variable.
b. Write an expression in terms of d for the number of dishes Julie washed.
c. Write an expression in terms of d for the number of minutes Julie has
been washing dishes.
d. Write an expression for the number of dishes Julie washed.
e. How many dishes has Dina washed after she has worked for 10 minutes?
f. How long has Dina been working when she finishes her 30th dish?
g. How many dishes has Julie washed if Dina has been washing dishes for
10 minutes?
h. How long has Dina been washing dishes if she and Julie have washed a
total of 240 dishes?
i. Write an equation to find out how long Dina has been washing dishes
when she and Julie have washed the same number of dishes.
j. How many dishes did the girls wash together if they quit when they had
both washed the same number of dishes?