Math 9Lesson #23 – Absolute Value Equations and

Inequalities

Mrs. Goodman

Solving an Absolute Value Equation

|x + 5| = 4

x + 5 = 4 x + 5 = -4

Solve each

x + 5 = 4 x + 5 = -4 -5 -5 -5 -5

x = -1 x = -9

|3x + 1| + 8 = 10

|3x + 1| = 23x + 1 = 2 3x + 1 = -2

-1 -1 -1 -1

3x = 1 3x = -3 3 3 3 3

x = 1/3 x = -1

Solving an Absolute Value Inequality

|x + 5| < 4

x + 5 < 4 x + 5 > -4

Solving an Absolute Value Inequality

|x + 3| < 7

x + 3 < 7 x + 3 > -7

Solving an Absolute Value Inequality

|x -2| > 8

x - 3 > 8 x - 3 < -8

Solving an Absolute Value Inequality

|x + 3| > 8

x + 3 > 8 x + 3 < -8

Solving an Absolute Value Inequality

• If you are solving a “less than” or “less than or equal to” absolute value inequality, the graph of your solution will look like an “and” inequality graph.

Solving an Absolute Value Inequality

• If you are solving a “greater than” or “greater than or equal to” absolute value inequality, the graph of your solution will look like an “or” inequality graph.

Solve

|2x – 5| < 42x – 5 < 4 2x – 5 > -

4 +5 +5 +5 +5 2x < 9 2x > 1 2 2 2 2 x < 9/2 AND x > 1/2

Solve

|-2x – 4| > 3-2x – 4 > 3 -2x – 4 < -

3 +4 +4 +4 +4 -2x > 7 -2x < 1 -2 -2 -2 -2 x < -7/2 OR x > -1/2

Try these on your own!

1. 3|4x + 1| = 102. |5x| + 1 > 163. |x – 11| < 214. 2|-2x – 7| = 20

That’s all for the day!

Thanks for working hard!

I’ll see you next time!