Maths Extension 1 Year 11 - Module 1 - Lesson 4
Absolute Value Inequalities
Name
Date
Class
1. Lesson focus
Absolute-value inequalities. Translate |u|<a to −a<u<a and |u|>a to u<−a or u>a; absolute value is never negative.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Solve |2x+1|>5.
3. Solve |x−4|+2=7.
3. Challenge
Solve |2x−3|=|x+2|.
4. Multiple choice
The inequality |x+1|<2 is equivalent to what?
A. −1<x<2
B. x<−3 or x>1
C. −3<x<1
D. −2<x<2
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Solve |x−2|≤3.
−3≤x−2≤3; adding 2 gives −1≤x≤5.
2. Solve |2x+1|>5.
2x+1>5 or 2x+1<−5, so x>2 or x<−3.
3. Solve |x−4|+2=7.
|x−4|=5, giving x−4=±5; x=−1 or x=9.
Challenge. Solve |2x−3|=|x+2|.
Square both sides: (2x−3)²=(x+2)²; difference of squares gives (x−5)(3x−1)=0, so x=5 or 1/3.
Multiple choice. The inequality |x+1|<2 is equivalent to what?
Correct answer: C. Subtract 1 from −2<x+1<2 to get −3<x<1.
Want help with Worksheet - Absolute Value Inequalities?
Tell us what you would like help with. Register interest; support details will be confirmed before enrolment.
Register interest →