1. Solving Compound and Absolute Value Inequalities
Chapter 1 – Section 6

2. Compound Inequalities
Compound Inequality – a pair of inequalities joined by and or or
Ex: -1 < x and x ≤ 3 which can be written as < x ≤ 3
x < -1 or x ≥ 3
For and statements the value must satisfy both inequalities
For or statements the value must satisfy one of the inequalities

3. And Inequalities
Graph the solution of 3x – 1 > -28 and 2x + 7 < 19.
3x > -27 and 2x < 12
x > -9 and x < 6

4. And Inequalities b)Graph the solution of -8 < 3x + 1 <19

5. Or Inequalities
ALGEBRA 2 LESSON 1-4
Graph the solution of 3x + 9 < –3 or –2x + 1 < 5.
3x + 9 < –3 or –2x + 1 < 5
3x < – –2x < 4
x < –4 or x > –2

6. Try These Problems
Graph the solution of 2x > x + 6 and x – 7 < 2
x > 6 and x < 9
Graph the solution of x – 1 < 3 or x + 3 > 8
x < 4 or x > 11

7. Absolute Value Inequalities
Let k represent a positive real number
│x │ ≥ k is equivalent to x ≤ -k or x ≥ k
│x │ ≤ k is equivalent to -k ≤ x ≤ k
Remember to isolate the absolute value before rewriting the problem with two inequalities

8. |2x – 5| > 3 2x < 2 2x > 8 Solve for x. x < 1 or x > 4
Solve |2x – 5| > 3. Graph the solution.
|2x – 5| > 3
2x – 5 < –3 or 2x – 5 > 3 Rewrite as a compound inequality.
2x < 2 2x > Solve for x.
x < 1 or x > 4

9. Try This Problem Solve │2x - 3 │ > 7
2x – 3 > or x – 3 < -7
2x > or x < -4
x > or x < -2

10. Solve –2|x + 1| + 5 –3. Graph the solution.
> –
–2|x + 1| –3
> –
–2|x + 1| –8 Isolate the absolute value expression. Subtract 5 from each side.
> –
|x + 1| 4 Divide each side by –2 and reverse the inequality.
< –
–4 x Rewrite as a compound inequality.
< –
–5 x 3 Solve for x.
< –

11. Try This Problem Solve |5z + 3| - 7 < 34. Graph the solution.

12. Homework
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