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Let’s look at the following equations.

X - 5 = 10

In order to solve an equation with a variable, we need to make the expressions have the same value. Here, clearly X cannot equal 10 because 10 - 5 would be “5”. So how do we make the “X” equal “10”?

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 - 5”. As this shows the number “5” is being subtracted from “X” we must add 5 to 5 as follows:

X - 5 + 5

(NOTE: If 5 was being added in the first expression, then we would have to subtract 5 as follows: X + 5 – 5)

We must then do the equal math to the known express of “10” as follows:

10 + 5

The new equation will now look as follows:

X - 5 + 5 = 10 + 5

We now add 10 + 5 = 15 and that makes the value of “X” equal 15.

15 - 5 = 10 so X = 15

However, sometimes we are faced with a different variable such as 7X = 21. When we see this type of equation, we will need to 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:

7X = 21 becomes X = 21 ÷ 7

21 ÷ 7 = 3

7 x 3 = 21

X = 3

1.

36X = 432

24

396

112

12

2.

2X = 366

83

93

133

183

2X = 366 ÷ 2

366 ÷ 2 = 183

183 x 2 = 366

X = 183

366 ÷ 2 = 183

183 x 2 = 366

X = 183

3.

18X = 504

18

28

38

48

18X = 504 ÷ 18

504 ÷ 18 = 28

28 x 18 = 504

X = 28

504 ÷ 18 = 28

28 x 18 = 504

X = 28

4.

8X = 40

6

320

32

5

8X = 40 ÷ 8

40 ÷ 8 = 5

5 x 8 = 40

X = 5

40 ÷ 8 = 5

5 x 8 = 40

X = 5

5.

22X = 594

572

27

52

157

22X = 594 ÷ 22

594 ÷ 22 = 27

27 x 22 = 594

X = 27

594 ÷ 22 = 27

27 x 22 = 594

X = 27

6.

25X = 400

16

26

6

36

25X = 400 ÷ 25

400 ÷ 25 = 16

16 x 25 = 400

X = 16

400 ÷ 25 = 16

16 x 25 = 400

X = 16

7.

10X = 100

100

10

1000

1

10X = 100 ÷ 10

100 ÷ 10 = 10

10 x 10 = 100

X = 10

100 ÷ 10 = 10

10 x 10 = 100

X = 10

8.

14X = 98

42

84

7

1372

14X = 98 ÷ 14

98 ÷ 14 = 7

7 x 14 = 98

X = 7

98 ÷ 14 = 7

7 x 14 = 98

X = 7

9.

9X = 117

13

1053

23

43

9X = 117 ÷ 9

117 ÷ 9 = 13

13 x 9 = 117

X = 13

117 ÷ 9 = 13

13 x 9 = 117

X = 13

10.

123X = 1107

19

21

9

27

123X = 1107 ÷ 123

1107 ÷ 123 = 9

9 x 123 = 1107

X = 9

1107 ÷ 123 = 9

9 x 123 = 1107

X = 9

432 ÷ 36 = 12

12 x 36 = 432

X = 12