# Solving Compound and Absolute Value Inequalities

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Solving Compound and Absolute Value Inequalities
Chapter 1 – Section 6

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

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

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

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

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

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

|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

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

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. <

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

Homework p. 44 #