➕ Algebra 1 · Inequalities
Absolute Value Equations cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The idea
- |x| = distance from 0, never negative
- |x − c| = distance from c
- Distance tells “how far,” not “which way”
The plan (BARS)
- B: Bars alone (isolate the absolute value)
- A: Ask about the number on the right
- R: Rewrite as two equations (inside = c or −c) when the number is positive
- S: Solve both, check both
How many solutions
- |A| = positive number: two solutions
- |A| = 0: one solution, A = 0
- |A| = negative number: no solution
Example
- 3|x + 4| − 6 = 15
- 3|x + 4| = 21 (add 6)
- |x + 4| = 7 (divide by 3)
- x + 4 = 7 or x + 4 = −7
- x = 3 or x = −11
Formulas
- Two solutions: |A| = c with c > 0 gives A = c or A = −c
- One solution: |A| = 0 gives A = 0
- No solution: |A| = c with c < 0 has no solution
- Distance form: |x − c| = d with d > 0 gives x = c − d or x = c + d
Absolute Value Equations cheat sheet from HighSchoolQ.com, for personal study use.