Math Journal 10-14Solve for x.

1. 2.

Solve the inequality for x, make a number line and graph the solu-tion.

3. 4.

Unit 3 Day 6: Solving Multi-Step Inequalities

Essential Question: How do I solve inequalities that require more than two

steps?

Process/StepsSIMPLIFY:

1) Apply the distributive property, if necessary

2) Combine like terms on each side

Isolate the variable and SOLVE by:

3) Drawing a line under the inequality sign

4) Undo addition or subtraction

5) Undo multiplication or division. If you used a negative number, FLIP THE INEQUALITY SIGN!!

ALWAYS:

6) Plug in and check your solution!

Example 1: Solve the inequality.

x - 3 > -9 -35

+ 3 + 3

-35

x > -6 · 5 5 ·

-3x > -30

-3 -3

x < 10

To get rid of a fraction:

1) Multiply by the denominator2) Divide by the numerator

OR

Multiply by the reciprocal

Example 2: Solve the inequality. Check your solutions.

7x – 3x – 8 < 24 4x – 8 + x > 2

4x - 8< 24+ 8 + 8

4x< 32

4 4x< 8

5x - 8> 2+ 8 +8

5x> 10

5 5x> 2

Example 3: Solve the inequality. Check your solutions.

2x – 9x + 17 > -4 4x – 9 + 3x < 5

-7x+ 17> -4

- 17 - 17

-7x> -21

-7 -7

x< 3

7x - 9< 5

+ 9 + 9

7x< 14

7 7

x< 2

Example 4: Solve the inequality.

5x + 3(x + 4) > 28 4x – 3(x – 2) < 21

5x+ 3x+ 12> 28

8x+ 12> 28-12 - 12

8x> 16

8 8

x > 2

4x- 3x+ 6< 21

x + 6< 21-6 - 6

x< 15

Example 5: Solve the inequality.

4x + 12(x - 3) < 28 2x – 5(x – 9) > 27

4x+ 12x- 36< 28

16x- 36 < 28

+36 +36

16x< 64

2x- 5x+ 45> 27

-3x+ 45> 27

- 45 -45

-3x> - 18

16 16

x< 4

-3 -3

x< 6

Summary

Essential Questions: How do I solve inequalities that require more than two steps?

Take 1 minute to write 2 sentences answering the essential questions.