1. Day Problems For each solution write and graph an inequality.
All real numbers n that are at most 6 or at least 10.
All real numbers x that are less than 5 or greater than 12.
Solve each compound inequality. Graph your solution.
k > 3 or 6k < – a < 1 or 3a ≤ 12
5. 5y + 7 ≤ -3 or 3y – 2 ≥ 13

2. 3.6 Absolute Value Equations and Inequalities
Solving an Absolute Value Equation
Solve | x | + 5 = 11
| x | + 5 = 11
| x | = 6
x = 6 or x = -6

3. Solving an Absolute Value Equation
Solve 4 | d | = 20.
4 | d | = 20
4d = 20
d = 5
So, d = 5 or d = -5.
4d = -20
d = -5

4. Solving Absolute Value Equations
To solve an equation in the form | A | = b, where A represents a variable expression and b > 0, solve A = b and A = -b.

5. Solving an Absolute Value Equation
Solve | 2p + 5 | = 11.
| 2p + 5 | = 11
2p + 5 = 11
2p = 6
p = 3
So, p = 3 or p = -8.
2p + 5 = -11
2p = -16
p = -8

6. 3.6 Absolute Value Equations and Inequalities (Cont.) 11/17/10
Solving Absolute Value Inequalities
To solve an inequality in the form | A | < b, where A is a variable expression and b > 0, solve -b < A < b.
To solve an inequality in the form | A | > b, where A is a variable expression and b > 0, solve A < -b or A > b.
Similar rules are true for | A | ≤ b or | A | ≥ b.

7. Solving an Absolute Value Inequality
Solve | v – 3 | ≥ 4.
v – 3 ≤ -4
v ≤ -1
So, v ≤ -1 OR v ≥ 7.
v – 3 ≥ 4
v ≥ 7 -7 -5 -3 -1 1 3 5 7 9

8. Solving an Absolute Value Inequality
Solve | x + 3 | < 5.
- 5 < x + 3 < 5
-5 < x + 3
-8 < x
So, -8 < x < 2.
x + 3 < 5
x < 2
-10 -8 -6 -4 -2 2 4 6 8 10

9. More Practice!!!!!
Homework – Textbook p. 169 – 170 # 2 – 34 even.