Download presentation
Presentation is loading. Please wait.
1
3-7 Solving Absolute Value Inequalities
2
Absolute Value (of x) Symbol lxl
The distance x is from 0 on the number line. Always positive Ex: l-3l=3
3
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.
4
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
5
How can I remember which inequality sign means what?
When dealing with absolute value inequalities, the rule is always… > Great“OR” < Less th“AND”
6
Great“OR” Less th“AND”
7
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
8
Solve. Then graph the solution set.
𝒙 +𝟏𝟕>𝟐𝟎 −𝟏𝟕 −𝟏𝟕 𝒙 >𝟑 𝑮𝒓𝒆𝒂𝒕“𝒐𝒓” 𝒙>𝟑 𝒐𝒓 𝒙<−𝟑
9
Solve. Then graph the solution set.
𝟒|𝒙|≤𝟑𝟔 𝟒 𝟒 |𝒙|≤𝟗 𝒍𝒆𝒔𝒔 𝒕𝒉“𝒂𝒏𝒅” −𝟗≤𝒙≤𝟗 Example 5-3b
10
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
11
𝟐𝒙 −𝟒>𝟒 +𝟒 +𝟒 𝟐𝒙 >𝟖 𝑮𝒓𝒆𝒂𝒕“𝒐𝒓” 𝟐𝒙>𝟖 𝒐𝒓 𝟐𝒙<−𝟖 𝟐 𝟐 𝟐 𝟐 𝒙>𝟒 𝒐𝒓 𝒙<−𝟒
12
Assignment: Due at the end of class!!!
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.