# Math: Middle School: Grades 6, 7 and 8 Quiz - Equations with Variables (Add and Subtract) (Questions)

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This quiz looks at more complex equations. Examine the following examples.

X - 4 = 8

In order to solve an equation with a variable, we need to make the expressions have the same value. Here, clearly X cannot equal 8 because 8 - 4 would be “4”. So how do we make the “X” equal “8”?

In a variable equation we must either add or subtract the known number in the unknown expression. In the above equation the unknown expression is “X - 4”. As this shows the number “4” is being subtracted from “X” we must add 4 to 4 as follows:

X - 4 + 4

(NOTE: If 4 was being added in the first expression, then we would have to subtract 4 as follows: X + 4 - 4)

We must then do the equal math to the known express of “8” as follows:

8 + 4

The new equation will now look as follows:

X - 4 + 4 = 8 + 4

We now add 8 + 4 = 12 and that makes the value of “X” equal 12.

12 - 4 = 8 so X = 12

1. X + 5 = 33
 [ ] 38 [ ] 28 [ ] 27 [ ] 37
2. X - 14 = 85
 [ ] 81 [ ] 71 [ ] 99 [ ] 89
3. X - 36 = 61
 [ ] 97 [ ] 25 [ ] 87 [ ] 85
4. X + 24 = 39
 [ ] 63 [ ] 5 [ ] 25 [ ] 15
5. X + 11 = 41
 [ ] 20 [ ] 52 [ ] 30 [ ] 32
6. X - 94 = 146
 [ ] 260 [ ] 240 [ ] 230 [ ] 250
7. X - 67 = 52
 [ ] 119 [ ] 109 [ ] 99 [ ] 17
8. X + 13 = 54
 [ ] 67 [ ] 31 [ ] 41 [ ] 27
9. X + 83 = 159
 [ ] 242 [ ] 42 [ ] 66 [ ] 76
10. X - 132 = 0
 [ ] 264 [ ] 132 [ ] -132 [ ] 0
Math: Middle School: Grades 6, 7 and 8 Quiz - Equations with Variables (Add and Subtract) (Answers)
1. X + 5 = 33
 [ ] 38 [x] 28 [ ] 27 [ ] 37
X + 5 - 5 = 33 - 5
33 - 5 = 28
28 + 5 = 33
X = 28
2. X - 14 = 85
 [ ] 81 [ ] 71 [x] 99 [ ] 89
X - 14 + 14 = 85 + 14
85 + 14 = 99
99 - 14 = 85
X = 99
3. X - 36 = 61
 [x] 97 [ ] 25 [ ] 87 [ ] 85
X - 36 + 36 = 61 + 36
61 + 36 = 97
97 - 36 = 61
X = 97
4. X + 24 = 39
 [ ] 63 [ ] 5 [ ] 25 [x] 15
X + 24 - 24 = 39 - 24
39 - 24 = 15
15 + 24 = 39
X = 15
5. X + 11 = 41
 [ ] 20 [ ] 52 [x] 30 [ ] 32
X + 11 - 11 = 41 - 11
41 - 11 = 30
30 + 11 = 41
X = 30
6. X - 94 = 146
 [ ] 260 [x] 240 [ ] 230 [ ] 250
X - 94 + 94 = 146 + 94
146 + 94 = 240
240 - 94 = 146
X = 240
7. X - 67 = 52
 [x] 119 [ ] 109 [ ] 99 [ ] 17
X - 67 + 67 = 52 + 67
52 + 67 = 119
119 - 67 = 52
X = 119
8. X + 13 = 54
 [ ] 67 [ ] 31 [x] 41 [ ] 27
X + 13 - 13 = 54 - 13
54 - 13 = 41
41 + 13 = 54
X = 41
9. X + 83 = 159
 [ ] 242 [ ] 42 [ ] 66 [x] 76
X + 83 - 83 = 159 - 83
159 - 83 = 76
76 + 83 = 159
X = 76
10. X - 132 = 0
 [ ] 264 [x] 132 [ ] -132 [ ] 0
X - 132 + 132 = 0 + 132
0 + 132 = 132
132 - 132 = 0
X = 132