Download presentation

Published byQuentin Hutchinson Modified over 4 years ago

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 p. 44 #

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google