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

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An example of an equation is X = Y. The letters “X” and “Y” are often referred to as “expressions” and are joined together using the equal “=” sign. The expression on both sides of the equal sign will have the same value. Sometimes an expression may contain a variable. Let’s look at the following equations.

X - 7 = 14

In order to solve an equation with a variable, we need to make the expressions have the same value. Here, clearly X cannot equal 14 because 14 - 7 would be “7”. So how do we make the “X” equal “14”?

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 - 7”. As this shows the number “7” is being subtracted from “X” we must add 7 to 7 as follows:

X - 7 + 7

We must then do the equal math to the known express of “14” as follows:

14 + 7

The new equation will now look as follows:

X - 7 + 7 = 14 + 7

We now add 14 + 7 = 21 and that makes the value of “X” equal 21.

21 - 7 = 14 so X = 21

However, sometimes we are faced with a different variable such as 8X - 2 = 14. When we see this type of equation, we will need to take a number of steps. First we must add the known number in the unknown expression to itself, or: 8X - 2 + 2 and we must also add 2 to the known expression, i.e., 14 + 2. The equation will now look like the following:

8X - 2 + 2 = 14 + 2
8X - 2 + 2 = 8X
14 + 2 = 16
8X = 16

At this point we must then divide the number in the unknown express with the number in the known expression and then multiply the number found in the unknown expression with the answer. For example:

8X = 16 becomes X = 16 ÷ 8
16 ÷ 8 = 2
8 x 2 = 16
X = 2

1. 3X - 5 = 25
 [ ] 15 [ ] 10 [ ] 5 [ ] 8
2. 7X - 8 = 132
 [ ] 21 [ ] 140 [ ] 56 [ ] 20
3. 12X + 16 = 244
 [ ] 28 [ ] 19 [ ] 26 [ ] 13
4. 6X + 15 = 153
 [ ] 23 [ ] 33 [ ] 13 [ ] 43
5. 19X - 51 = 63
 [ ] 4 [ ] 5 [ ] 6 [ ] 7
6. 99X - 196 = 200
 [ ] 44 [ ] 114 [ ] 14 [ ] 4
7. 27X + 44 = 341
 [ ] 21 [ ] 11 [ ] 31 [ ] 33
8. 32X + 91 = 283
 [ ] 6 [ ] 16 [ ] 26 [ ] 36
9. 14X - 98 = 98
 [ ] 4 [ ] 24 [ ] 44 [ ] 14
10. 22X + 88 = 660
 [ ] 6 [ ] 16 [ ] 26 [ ] 36 1. 3X - 5 = 25
 [ ] 15 [x] 10 [ ] 5 [ ] 8
3X - 5 + 5 = 25 + 5
3X - 5 + 5 = 3X
25 + 5 = 30
3X = 30
30 ÷ 3 = 10
10 x 3 = 30
X = 10
2. 7X - 8 = 132
 [ ] 21 [ ] 140 [ ] 56 [x] 20
7X - 8 + 8 = 132 + 8
7X - 8 + 8 = 7X
132 + 8 = 140
7X = 140
140 ÷ 7 = 20
20 x 7 = 140
X = 20
3. 12X + 16 = 244
 [ ] 28 [x] 19 [ ] 26 [ ] 13
12X + 16 - 16 = 244 - 16
12X + 16 - 16 = 12X
244 - 16 = 228
12X = 228
228 ÷ 12 = 19
19 x 12 = 228
X = 19
4. 6X + 15 = 153
 [x] 23 [ ] 33 [ ] 13 [ ] 43
6X + 15 - 15 = 153 - 15
6X + 15 - 15 = 6X
153 - 15 = 138
6X = 138
138 ÷ 6 = 23
23 x 6 = 138
X = 23
5. 19X - 51 = 63
 [ ] 4 [ ] 5 [x] 6 [ ] 7
19X - 51 + 51 = 63 + 51
19X - 51 + 51 = 19X
63 + 51 = 114
19X = 114
114 ÷ 19 = 6
6 x 19 = 114
X = 6
6. 99X - 196 = 200
 [ ] 44 [ ] 114 [ ] 14 [x] 4
99X - 196 + 196 = 200 + 196
99X - 196 + 196 = 99X
200 + 196 = 396
99X = 396
396 ÷ 99 = 4
4 x 99 = 396
X = 4
7. 27X + 44 = 341
 [ ] 21 [x] 11 [ ] 31 [ ] 33
27X + 44 - 44 = 341 - 44
27X + 44 - 44 = 27X
341 - 44 = 297
27X = 297
297 ÷ 27 = 11
11 x 27 = 297
X = 11
8. 32X + 91 = 283
 [x] 6 [ ] 16 [ ] 26 [ ] 36
32X + 91 - 91 = 283 - 91
32X + 91 - 91 = 32X
283 - 91 = 192
32X = 192
192 ÷ 32 = 6
6 x 32 = 192
X = 6
9. 14X - 98 = 98
 [ ] 4 [ ] 24 [ ] 44 [x] 14
14X - 98 + 98 = 98 + 98
14X - 98 + 98 = 14X
98 + 98 = 196
14X = 196
196 ÷ 14 = 14
14 x 14 = 196
X = 14
10. 22X + 88 = 660
 [ ] 6 [ ] 16 [x] 26 [ ] 36
22X + 88 - 88 = 660 - 88
22X + 88 - 88 = 22X
660 - 88 = 572
22X = 572
572 ÷ 22 = 26
26 x 22 = 572
X = 26