 Equations with Variables (Multiply and Divide)

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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
36X = 432 ÷ 36
432 ÷ 36 = 12
12 x 36 = 432
X = 12
2.
2X = 366
83
93
133
183
2X = 366 ÷ 2
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
4.
8X = 40
6
320
32
5
8X = 40 ÷ 8
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
6.
25X = 400
16
26
6
36
25X = 400 ÷ 25
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
8.
14X = 98
42
84
7
1372
14X = 98 ÷ 14
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
10.
123X = 1107
19
21
9
27
123X = 1107 ÷ 123
1107 ÷ 123 = 9
9 x 123 = 1107
X = 9
Author:  Christine G. Broome

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