1. 0.4 Solving Linear Inequalities
8/31/2012

2. You have learned how to solve equations with 1 variable.
Ex. x + 3 = 7
x = 4
Ex. x - 5 = 2
x = 7
Ex. 3x = 12
x = 4
Ex y = 6 2
y = 12 ·2 2·

3. To solve inequality in 1 variable
All the rules apply for solving equations in 1 variable except when dividing or multiplying both sides by a negative number. Rule: When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality symbol.

4. Example 1 Solve the inequality. a. > x 4 – 6 SOLUTION a. > x 4 –
Inequality with a Variable on One Side
Solve the inequality. a.
> x – 6
SOLUTION a.
> x – 6
> x 2 –

5. Example 1
Inequality with a Variable on One Side b. – ≥ 5y 13 + – ≥ 5y 15 y ≤ 3 5

6. Example 2 Solve . < 7 4x 1 2x – < 7 2x – 1 < 2x – 6 > x 3
Inequality with a Variable on Both Sides
Solve
< x x –
+2x x
< x – 1
< 2x – 6
> x 3 6

7. Solve the inequality. Then graph your solution. ANSWER < x 3 8 + 1.
Extra Problems
Solve the inequality. Then graph your solution.
ANSWER
< x 8 + 1. x
< 5 5 ≤ x – 2. x ≥ – 1

8. Checkpoint Solve the inequality. 3 2 > 2x 1 – 3. ANSWER x > 2 –
Solve an Inequality
Solve the inequality. 3 2
>
2x 1 – 3.
ANSWER x
> 2 – x
> 2x 4. x
> 3

9. Example 3 Solve 3(4x +1 ) ≤ 15x + 12 12x +3 ≤ 15x +12 - 12x - 12x ≤ 3
Inequality with Distributive
Solve 3(4x +1 ) ≤ 15x + 12
12x +3 ≤ 15x +12
- 12x x ≤ 3
3x+12 ≤ 9 – 3x ≤ -3 x ≥ x -3 9

10. Solve the double inequalities.
Example 4
Solve Double Inequalities
Solve the double inequalities. 1. 4 x
< + 5 7
-1 < x < 2 2. 3x ≤ + 8 1 –
-9 ≤ 3x ≤ 0
≤ 0 – 3 ≤ x

11. Homework WS 0.4 #17-32, 35-38