# Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman.

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Math 9 Lesson #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| = 2 3x + 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

Solving an Absolute Value Inequality |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| < 4 2x – 5 -4 +5 +5 +5 +5 2x 1 2 2 2 2 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 -1/2

Try these on your own! 1.3|4x + 1| = 10 2.|5x| + 1 > 16 3.|x – 11| < 21 4.2|-2x – 7| = 20

That’s all for the day! Thanks for working hard! I’ll see you next time!

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