Solving Absolute Value Inequalities

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Presentation transcript:

Solving Absolute Value Inequalities What do you know about inequalities? Greater than Less than Greater than or equal to Less than or equal to

Solving Inequalities -3x < 6 divide both sides by -3 x > -2 To solve an inequality, use the same procedure as solving an equation with one exception: When multiplying or dividing by a negative number, reverse the direction of the inequality sign. -3x < 6 divide both sides by -3 -3x/-3 > 6/-3 x > -2

Solving Absolute Value Inequalities To solve an absolute value inequality: 1. Isolate the absolute value 2. Look at the inequality symbol and determine and vs or: Less th “and” Great “or” Set up 2 inequalities. For the second inequality, you have to negate the right side of the inequality and reverse the inequality sign. Solve and graph appropriately.

Example 1: Solve: |2x + 4| > 12 2x + 4 > 12 or 2x + 4 < -12 2x > 8 2x < -16 x > 4 or x < -8 x < -8 or x > 4 4 -8

Example 2: Solve: 2|4 - x| < 10 4 - x < 5 and 4 - x > -5 - x < 1 - x > -9 x > -1 and x < 9 -1 < x < 9 9 -1