Equations with Added Variables

Can you count how many times the number 6 appears in this quiz?

Equations with Added Variables

This Math quiz is called 'Equations with Added Variables' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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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.
99X - 196 = 200
44
114
14
4
99X - 196 + 196 = 200 + 196
99X - 196 + 196 = 99X
200 + 196 = 396
99X = 396
396 ÷ 99 = 4
4 x 99 = 396
X = 4
2.
22X + 88 = 660
6
16
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
3.
3X - 5 = 25
15
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
4.
12X + 16 = 244
28
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
5.
19X - 51 = 63
4
5
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.
7X - 8 = 132
21
140
56
20
7X - 8 + 8 = 132 + 8
7X - 8 + 8 = 7X
132 + 8 = 140
7X = 140
140 ÷ 7 = 20
20 x 7 = 140
X = 20
7.
14X - 98 = 98
4
24
44
14
14X - 98 + 98 = 98 + 98
14X - 98 + 98 = 14X
98 + 98 = 196
14X = 196
196 ÷ 14 = 14
14 x 14 = 196
X = 14
8.
6X + 15 = 153
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
9.
27X + 44 = 341
21
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
10.
32X + 91 = 283
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
Author:  Christine G. Broome

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