MULTI-STEP INEQUALITIESChapter 6.4

MULTI-STEP INEQUALITIES Reminder: What are we trying to do

when we solve an inequality? Answer: To get the variable by itself

MULTI-STEP INEQUALITIES Example 1:

First we must get the term with the x by itself.

Subtract 3 from both sides Divide both sides by 2

2x+ 3<9- 3 - 3

62 2x 3

MULTI-STEP INEQUALITIES

1. 3x + 5 > 142. 6x + 2 ≤ 203. 23 ≥ 2x + 74. 8 + 3x > 325. - 9 < 3 + 4x

Practice

MULTI-STEP INEQUALITIES Example 2: ≤

Add 5 to both sides Divide both sides by 3

3x

- 5 7+5 +5

123 3x 4

MULTI-STEP INEQUALITIES

1. 2x – 5 > 72. 4x – 3 ≥ -153. 6 ≤ 5x – 94. -7 < 2x – 7

Practice

MULTI-STEP INEQUALITIES Example 3:

Subtract 3 from both sides Divide both sides by -2 Remember, when you divide both sides

by a negative you have to switch the sign

-2x

+ 3> 9-3 -3

6-2 -2

x -3

MULTI-STEP INEQUALITIES

1. -3x + 5 ≤ 172. -5x – 7 > 83. 7 – 4x ≥ 34. -8 ≤ 6 – 7x

Practice

MULTI-STEP INEQUALITIES Example 4:

Rewrite with the x on the top of the fraction

Multiply both sides by 3 Divide both sides by 2 Simplify

x >43 (3)

2x 122 2x 6

MULTI-STEP INEQUALITIES1. x > 9

2. x ≤ -6

3. -10 < - x

4. - ≥ 4

Practice3 23 4

5 2

6 7

MULTI-STEP INEQUALITIES Example 5:

To get the x by itself we have to get rid of the fraction first

Multiply both sides by 5 Subtract 3 from both sides Divide by 2

≥ 75 (5)2x + 3 35-3 -3

2x 322 2

x 16

MULTI-STEP INEQUALITIES1. ≥ 5

2. ≤ -6

3. -4 > -

4. < 7

Last Practice2x + 3

74x + 4

33x + 5

55 - 2x

3

MULTI-STEP INEQUALITIES1. 4x + 7 > - 52. 9 ≤ 7 – 6x3. -3x – 10 ≥ - 16

4. x ≤ -6

5. < 7

Quiz

3 42x + 5 3