Solving Multi-step Equations by Combining Like Terms

and withVariables on Both Sides

Simplifying equations involves three steps.

• Getting rid of fractions.– To get rid of a fraction from

an equation multiply each term by the LCD.

• Getting rid of parentheses.– To get rid of parentheses

from an equation, distribute.

• Getting rid of like terms that are on the same side of the equal sign.– Combine like terms by

adding or subtracting using your integer rules.

This lesson focuses onthis part.

Ex. 1 To SIMPLIFY use this checklist.

• Any fractions?– NO

• Any ( )– NO

• Any like terms– YES – use integer

rules.

• Now SOLVE

4 9 4x x 5x 45 5

x 4

5

Ex. 2To SIMPLIFY use this

checklist.

• Any fractions?– NO

• Any ( )– NO

• Any like terms– YES – Combine

them using Integer rules.

• Now ISOLATE the variable

• and SOLVE

3 2 10 8x x 3 2 8 10x x

10x 103 1010

10x71010

x7

10

Ex. 3To SIMPLIFY use this

checklist.• Any fractions?

– NO

• Any ( )– NO

• Any like terms– NO

• So ISOLATE the variables. Get them together on the same side

• Now SOLVE– And reduce

5 8 6x x xx

4x 8 6 8 8

4x 24 4

x 2

4

1

2x

Ex. 4To SIMPLIFY use this

checklist.• Any fractions?

– NO

• Any ( )– NO

• Any like terms– NO

• So ISOLATE the variables. Get them together on the same side

• Now SOLVE

3 5 7 21x x 7x7x

4x 5 21 5 5

4x 164 4

x 4

Ex. 5

5 21 7 21 2x x

To SIMPLIFY use this checklist.

• Any fractions?– NO

• Any ( )– NO

• Any like terms– YES – Regroup

then use integer rules.

• Now SOLVE

5 7x x 21 21 22x 42 2

42 42

2x 442 2

x 22

21x 4 14x 1 321 14x x 4 1 335x 3 3

3 3

35x 035 35

x 0

To SIMPLIFY use this checklist.

• Any fractions?– NO

• Any ( )– NO

• Any like terms– YES – Regroup

then use integer rules.

• Now ISOLATE• and SOLVE

Ex. 6