Pre-Algebra Demystified

Check:

3 ð2xþ 6 Þ¼ 30

3 ð 2  2 þ 6 Þ¼ 30

3  10 ¼ 30

30 ¼ 30

The procedure for solving equations in general is:

 Step 1 Remove parentheses.

 Step 2 Combine like terms on each side of the equation.

 Step 3 Use the addition and/or subtraction principle to get the variables

on one side and the constant terms on the other side.

 Step 4 Use the division principle to solve for x.

 Step 5 Check the equation.

EXAMPLE

Solve 5(2x
7)
3x¼5xþ9.

SOLUTION

5 ð2x
 7 Þ
3x¼5xþ 9

10x
 35 
3x¼5xþ 9 Remove parentheses

7x
 35 ¼5xþ 9 Combine like terms

7x
 35 
5x¼5x
5xþ 9 Get variables on one side and the

2x
 35 ¼ 9 constants on the other side

2x
 35 þ 35 ¼ 9 þ 35

2x¼ 44

2 x

2

¼

44

2

Divide by 2

x¼ 22

Check:

5 ð2x
 7 Þ
3x¼5xþ 9

5 ð 2  22 
 7 Þ
 3  22 ¼ 5  22 þ 9

5 ð 44 
 7 Þ
 66 ¼ 110 þ 9

5 ð 37 Þ
 66 ¼ 119

185 
 66 ¼ 119

119 ¼ 119

142 CHAPTER 7 Expression and Equations