1. Chapter 1.6 Solving Compound & Absolute Value Inequalities
Algebra 2
Chapter 1.6
Solving Compound & Absolute Value Inequalities
Target Goals:
Solve compound inequalities
Solve absolute value inequalities

2. Compound Inequalities
2 inequalities joined by “and” or “or” (sometimes with words, sometimes with symbols)
2 Types:
“And” Compound Inequalities
“Or” Compound Inequalities
You will always have 2 inequalities!!!

3. “And” Compound Inequalities
The compound inequality is true if both of its equalities are true.
When looking at the graph, this is where the shading intersects.

4. Ex 1) Solve and and Method 1: Solve separately
Method 2: Solve together
and
and

5. Ex 1) Graph the solution set on a number line and express the solution in interval notation.-5 6 -5 6 -5 6
Interval Notation: [-5, 6)

6. “Or” Compound Inequalities
The compound inequality is true if either of its equalities are true. Both don’t have to be true.
When looking at the graph, this is wherever the shading naturally falls.

7. [ Ex 2) Solve or Interval Notation: (-∞, -1) or [4, ∞) -1 4 “Solve.”4
“Graph the solution set on a number line.”
Interval Notation: (-∞, -1) or [4, ∞)
“Express the solution in interval notation.”

8. Absolute Value Inequalities
Absolute value inequality
Which compound inequality?
Great”or”
Less th”and”

9. ( ) Interval Notation: (-2, 2)
Ex 3) Solve Graph the solution set on a number line and express the solution in interval notation.
“and” or “or”?
2 inequalities?
AND
d < 2 and –d < 2
d < 2 and d > -2 ( ) -2 2
Interval Notation: (-2, 2)

10. ] [ Interval Notation: (-∞, -3] or [3, ∞) “and” or “or”?
Ex 4) Solve . Graph the solution set on a number line and express the solution in interval notation.
“and” or “or”?
2 inequalities? OR
d ≥ 3 or –d ≥ 3
d ≥ 3 or d ≤ -3 ] [ -3 3
Interval Notation: (-∞, -3] or [3, ∞)

11. ) ( Interval Notation: (-∞, -3/2) or (5, ∞) “and” or “or”?
Ex 5) Solve . Graph the solution set on a number line and express the solution in interval notation.
“and” or “or”?
2 inequalities? OR
4x – 7 > 13 or -4x + 7 > 13
4x > 20
-4x > 6
x > 5
x < -3/2
x > 5 or x < -3/2 ) (
-3/2 5
Interval Notation: (-∞, -3/2) or (5, ∞)

12. [ ] Interval Notation: [-19/5, 3]
Ex 6) Solve Graph the solution set on a number line and express the solution in interval notation.
“and” or “or”?
2 inequalities?
AND
5y + 2 ≤ 17 and –5y – 2 ≤ 17
5y ≤ 15
-5y ≤ 19
y ≤ 3
y ≥ -19/5 [ ]
y ≤ 3 and y ≥ -19/5
-19/5 3
Interval Notation: [-19/5, 3]

13. Extention/Challenge ) (
What type of solution would you have if you have an “and” and no shading intersects on the graph?
No solution! ) (

14. Extention/Challenge [ ]
What type of solution would you have if you have an “or” and the entire line has been shaded?
Infinitely many solutions or all real numbers [ ]

15. Target Goals Solve compound inequalities
(ex 1-6)
Solve absolute value inequalities
(ex 3-6)