Chapter 2

2.3 Solving Multi- Step Equations

Solving Multi-Steps Equations

1. Clear the equation of fractions and decimals.

2. Use the Distribution Property to remove parentheses on each side.

3. Combine like terms on each side.

4. Undo addition or subtraction.

5. Undo multiplication or division.

2𝑐+𝑐+12=78

Example 1a.

3𝑐+12=78 Combine like terms

3𝑐+12−12=78−12 Subtract 12 from each side

3𝑐=66 Simplify

3𝑐3

=663

𝑐=22

Divide each side by 3

Simplify

4𝑏+16+2𝑏=46

Example 1b.

6𝑏+16=46 Combine like terms

6𝑏+16−16=46−16 Subtract 12 from each side

6𝑏=30 Simplify

6𝑏6

=306

𝑏=5

Divide each side by 6

Simplify

4𝑏+2𝑏+16=46 Use the Commutative Property of Addition

−2 (𝑏−4)=12

Example 3.

−2𝑏+8−8=12−8 Subtract 8 from each side

−2𝑏=4 Simplify

−2𝑏−2

=4−2

𝑏=−2

Divide each side by -2

Simplify

−2𝑏+8=12 Use the Distributive Property

Grouping in an equation

2𝑥3

+𝑥2

=7

Example 4a.

Write the fractions with a denominator of 6

Simplify

𝑥=6

Divide each side by 6/7

Simplify

Rewrite the fractions with as coefficients

Fractions in an equation

23𝑥+12𝑥=7

46𝑥+36𝑥=7

76𝑥=7

(

Method I Adding

Fractions.

2𝑥3

+𝑥2

=7

Example 4b.

Use the Distributive Property

Multiply

𝑥=6

Combine like terms

Simplify

Mulitply each side by 6 a common multiple of 3 and 2.

Fractions in an equation

7x

Method II Multiplying to

clear fractions.

6 (2𝑥3

+𝑥2

)=7 ∙6

6 (2𝑥3

)+6 (𝑥2)=7 ∙6

7𝑥7

=427

Divide each side by 7

Do problems 2,4,12,14,22,24

Page 91

You have 25 minutes then we will check answers

Problem # Answer

2 8

4 3

12 3

14 -2

22 1 1/2

24 7

HomeworkPage 911- 9 odd

12- 29 odd