Transcript 4.5.1 * Solving Absolute Value Inequalities

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. 201
• 5-10, 21-29 odd, 34-38, 46, 48