1. Warm Up
Solve each inequality.
1. x + 3 ≤ 10 2.
x ≤ 7
23 < –2x + 3
x < –10
Solve each inequality and graph the solutions.
4. 4x + 1 ≤ 25
x ≤ 6
5. 0 ≥ 3x + 3
x ≤ –1

2. Solving compound Inequalities
Lesson 2-6
Solving compound Inequalities
You'll Learn how to
solve compound inequalities.
graph the solution sets of compound inequalities.

3. Which of these applicants meet the requirements?
RPS will hire a new Teacher that’s tall AND good looking
Alex: 166 cm
John: 186 cm
Sam: 183 cm
Which of these applicants meet the requirements?
He is tall AND good looking

4. Which of these applicants meet the requirements?
RPS will hire a new Teacher that’s tall OR good looking
Alex: 166 cm
John: 186 cm
Sam: 183 cm
Which of these applicants meet the requirements?
All of them
Every applicant is either tall OR Good looking

5. Definition
A compound inequality consists of two inequalities connected by the words:
AND
(conjunction) OR
(disjunction)

6. 1 solve compound inequalities (conjunction/and) 3x – 5 > 7 and
EXAMPLE 1
Solve and graph
3x – 5 > 7
and
8x – 14 ≤ 66
Solve both inequalities for x 8x ≤ 66
+ 14 3x
> 7
+ 5 8x ≤ 80 3x
> 12 8 8 3 3 x ≤ 10 x
> 4
Graph the solution
The Solution is the (double shaded) region 2 –6 –4 –2 6 4 –8 8 10 12
–10
–12 4
< x ≤ 10

7. Solve the conjunction for x
EXAMPLE 2
Solve and graph
-1 < x + 3 < 2
Solve the conjunction for x -3 -3 -3 -4
< x
< -1
Graph the solution 1 –3 –2 –1 3 2 –4 4 5 6 –5 –6

8. 3 solve compound inequalities (disjunction/or) 2x + 3 < –7 Or
EXAMPLE 3
Solve and graph
2x + 3 < –7 Or
4x – 10 ≥ – 2
Solve both inequalities for x 4x ≥ –2
+ 10 2x
< –7
– 3 4x ≥ 8 2x
<
-10 4 4 2 2 x ≥ 2 x
< -5
Graph the solution
The Solution is (All shaded) regions 1 –3 –2 –1 3 2 –4 4 5 6 –5 –6

9. -2x + 1 ≥ 3 and 3x – 4 ≤ 17 x – 2 > – 4 or x + 2 < 5
Your Turn
Solve and graph 1
-2x + 1 ≥ 3
and
3x – 4 ≤ 17 2
x – 2 > – 4 or
x + 2 < 5 3
-5 < 2x – 3 ≤ 11

10. Homework
Page 138 – 139 #s:
16-all-26, 36-all , 49 and 50