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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.

7X - 8 = 132

21

140

56

20

2.

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

3X - 5 + 5 = 3X

25 + 5 = 30

3X = 30

30 ÷ 3 = 10

10 x 3 = 30

X = 10

3.

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

22X + 88 - 88 = 22X

660 - 88 = 572

22X = 572

572 ÷ 22 = 26

26 x 22 = 572

X = 26

4.

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

27X + 44 - 44 = 27X

341 - 44 = 297

27X = 297

297 ÷ 27 = 11

11 x 27 = 297

X = 11

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

19X - 51 + 51 = 19X

63 + 51 = 114

19X = 114

114 ÷ 19 = 6

6 x 19 = 114

X = 6

6.

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

6X + 15 - 15 = 6X

153 - 15 = 138

6X = 138

138 ÷ 6 = 23

23 x 6 = 138

X = 23

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

14X - 98 + 98 = 14X

98 + 98 = 196

14X = 196

196 ÷ 14 = 14

14 x 14 = 196

X = 14

8.

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

12X + 16 - 16 = 12X

244 - 16 = 228

12X = 228

228 ÷ 12 = 19

19 x 12 = 228

X = 19

9.

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

32X + 91 - 91 = 32X

283 - 91 = 192

32X = 192

192 ÷ 32 = 6

6 x 32 = 192

X = 6

10.

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

99X - 196 + 196 = 99X

200 + 196 = 396

99X = 396

396 ÷ 99 = 4

4 x 99 = 396

X = 4

7X - 8 + 8 = 7X

132 + 8 = 140

7X = 140

140 ÷ 7 = 20

20 x 7 = 140

X = 20