3-7 Solving Absolute Value Inequalities

Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=3 -4 -3 -2 -1 0 1 2

Things to Remember… When a variable is inside the absolute value bars, there will be 2 solutions. When an absolute value is set equal to a negative number, there is no solution. The only situation where there would be one solution when solving absolute value equations is when the absolute value is set equal to 0.

To solve an absolute value inequality: ax+b > c To solve: ISOLATE THE ABSOLUTE VALUE Set up 2 new inequalities -one with a positive and one with a negative -flip the NEGATIVE inequality

How can I remember which inequality sign means what? When dealing with absolute value inequalities, the rule is always… > Great“OR” < Less th“AND”

Great“OR” Less th“AND”

x  2  3 +𝟐 +𝟐 |𝒙|≤𝟓 −𝟓≤𝒙≤𝟓 Solve. Then graph the solution set. +𝟐 +𝟐 |𝒙|≤𝟓 −𝟓≤𝒙≤𝟓 Example 5-3a

Solve. Then graph the solution set. 𝒙 +𝟏𝟕>𝟐𝟎 −𝟏𝟕 −𝟏𝟕 𝒙 >𝟑 𝑮𝒓𝒆𝒂𝒕“𝒐𝒓” 𝒙>𝟑 𝒐𝒓 𝒙<−𝟑

Solve. Then graph the solution set. 𝟒|𝒙|≤𝟑𝟔 𝟒 𝟒 |𝒙|≤𝟗 𝒍𝒆𝒔𝒔 𝒕𝒉“𝒂𝒏𝒅” −𝟗≤𝒙≤𝟗 Example 5-3b

𝒙−𝟔 −𝟕>−𝟑 +𝟕 +𝟕 𝒙−𝟔 >𝟒 𝑮𝒓𝒆𝒂𝒕“𝒐𝒓” 𝒙−𝟔>𝟒 𝒐𝒓 𝒙−𝟔<−𝟒 +𝟔 +𝟔 +𝟔 +𝟔 𝒙>𝟏𝟎 𝒐𝒓 𝒙<𝟐

𝟐𝒙 −𝟒>𝟒 +𝟒 +𝟒 𝟐𝒙 >𝟖 𝑮𝒓𝒆𝒂𝒕“𝒐𝒓” 𝟐𝒙>𝟖 𝒐𝒓 𝟐𝒙<−𝟖 𝟐 𝟐 𝟐 𝟐 𝒙>𝟒 𝒐𝒓 𝒙<−𝟒

Assignment: Due at the end of class!!!