4.5.1 – Solving Absolute Value Inequalities

We’ve now addressed how to solve absolute value equations We can extend absolute value to inequalities Remember, the absolute value equation y = |x| is asking for the distance a number x is from zero (left or right)

Inequalities An absolute value inequality is asking for the values that will either be between certain numbers, or outside those numbers Two cases we will have to consider

Case 1 When given the absolute value inequality |ax + b| > c OR |ax + b| ≥ c, we will setup 2 inequalities to solve 1) ax + b > c (or ≥) OR 2) ax + b < -c (or ≤) Want to go further away on the distance

Example. Solve the absolute value inequality |x + 4| > 9 Two inequalities?

Example. Solve the absolute value inequality |2x – 5| ≥ 13 Two inequalities?

Case 2 The second case will involve staying between two values When given the absolute value inequality |ax + b| < c or |ax + b| ≤ c, we will set up the following inequality; -c < ax + b < c -c ≤ ax + b ≤ c

Example. Solve the absolute value inequality |x + 8| < 10 Inequality?

Example. Solve the absolute value inequality |-4 + 3x| ≤ 14 Inequality?

Application Example. The absolute value inequality |t – 98.4| ≤ 0.6 is a model for normal body temperatures of humans at time t. Find the maximum and minimum the internal temperature of a body should be.

Assignment Pg , odd, 34-38, 46, 48