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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.
[readmore]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
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7X - 8 + 8 = 132 + 8
7X - 8 + 8 = 7X 132 + 8 = 140 7X = 140 140 ÷ 7 = 20 20 x 7 = 140 X = 20 |
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12X + 16 - 16 = 244 - 16
12X + 16 - 16 = 12X 244 - 16 = 228 12X = 228 228 ÷ 12 = 19 19 x 12 = 228 X = 19 |
6X + 15 - 15 = 153 - 15
6X + 15 - 15 = 6X 153 - 15 = 138 6X = 138 138 ÷ 6 = 23 23 x 6 = 138 X = 23 |
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19X - 51 + 51 = 63 + 51
19X - 51 + 51 = 19X 63 + 51 = 114 19X = 114 114 ÷ 19 = 6 6 x 19 = 114 X = 6 |
99X - 196 + 196 = 200 + 196
99X - 196 + 196 = 99X 200 + 196 = 396 99X = 396 396 ÷ 99 = 4 4 x 99 = 396 X = 4 |
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27X + 44 - 44 = 341 - 44
27X + 44 - 44 = 27X 341 - 44 = 297 27X = 297 297 ÷ 27 = 11 11 x 27 = 297 X = 11 |
32X + 91 - 91 = 283 - 91
32X + 91 - 91 = 32X 283 - 91 = 192 32X = 192 192 ÷ 32 = 6 6 x 32 = 192 X = 6 |
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14X - 98 + 98 = 98 + 98
14X - 98 + 98 = 14X 98 + 98 = 196 14X = 196 196 ÷ 14 = 14 14 x 14 = 196 X = 14 |
22X + 88 - 88 = 660 - 88
22X + 88 - 88 = 22X 660 - 88 = 572 22X = 572 572 ÷ 22 = 26 26 x 22 = 572 X = 26 |
3X - 5 + 5 = 3X
25 + 5 = 30
3X = 30
30 ÷ 3 = 10
10 x 3 = 30
X = 10