1. 3.5 Compound Inequalities
Objective: SWBAT solve compound inequalities.

2. Mini Quiz 24 1. Solve 2x – 3 ≤ 5x + 9 2. Solve 2x – 4 ≤ 2(3x – 6)
2. Solve 2x – 4 ≤ 2(3x – 6)
3. Is -2 a solution to the inequality
x – 2 ≤ 5(x-1)

3. Quick Review 1. Evaluate |-4| 4 2. True or False: |-5| = -5 False
3. What two values can x equal for the equation |x| = 8
-8, 8
4. What is the distance of 3 and -2? 5

4. Compound Inequality
Compound Inequality - two inequalities connected by and or or (this is similar to compound sentences in English, which are joined by and, or, or but).
Example:
0 < x ≤ 4 (aka 0 < x and x ≤ 4)
x < -1 or x > 2 (or can’t be combined)
Note: it’s one way OR the other

5. Compound Inequality with “OR”
Solve and graph the solution
1. 3x + 1 < 4 or 2x – 5 > 7
3x < 3 or 2x > 12
x < 1 or x > 6

6. Compound Inequality with “AND”
Solve and Graph
≤ 3x – 8 ≤ 10
Method 1: Method 2:
-2 ≤ 3x – 8 ≤ ≤ 3x – 8 and 3x – 8 ≤ 10
6 ≤ 3x ≤ ≤ 3x and x ≤ 18
2 ≤ x ≤ ≤ x and x ≤ 6
2 ≤ x ≤ 6

7. Solving Compound Inequalities with “AND” and “OR”
Solve and Graph the inequalities
3. –2 < -2 – x < 1
0 > x > -3

8. Solving Compound Inequalities with “AND” and “OR”
Solve and Graph the inequalities
4. 2x + 3 < -1 or 3x – 5 > -2
x < -2 or x > 1

9. Solving Compound Inequalities with “AND” and “OR”
Solve and Graph the inequalities
5. 7 < 4 + x < 8
3 < x < 4

10. Solving Compound Inequalities with “AND” and “OR”
Solve and Graph the inequalities
< 2x + 3 ≤ 13
-2 < x ≤ 5

11. Solving Compound Inequalities with “AND” and “OR”
7. 4x – 1 > 7 or 5x – 1 < -6
x < 2 or x < -1

12. Wrap Up Compound Inequalities OR - solve each one separately
AND – isolate variable or break into two problems and solve each one separately
Graph your solution
HW: P #1-31 odd
Write DLUQ: How many problems do you need to solve in when you have a compound inequality?

13. T2L
Solve and Graph 1. 2.