LCAT Math, Advanced Math
Absolute value for the LCAT: lesson and practice
Absolute value is distance from zero, so it is never negative. |A| = b (with b > 0) means A = b or A = −b, which usually gives two solutions. |A| = a negative number has no solution. |x − a| < b means x is between a − b and a + b; > means outside that range.
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No calculator on the LCAT. LUMS’s official sample says calculators are not allowed, so every practice question here can be solved by hand.
| Form | Solution |
|---|---|
| |x − 3| = 5 | x = 8 or x = −2 |
| |x + 1| = −4 | No solution |
| |x − 2| < 3 | −1 < x < 5 |
| |x − 2| > 3 | x < −1 or x > 5 |
Common mistakes
Only one solutionWrite both equations: = b and = −b.
Ignoring a negative right sideAn absolute value can never equal a negative number.
Between vs outsideLess than: between. Greater than: outside.
Sample questions with answers
1. Solve |x − 3| = 5.
- x = 8 only
- x = 8 and x = −2 (correct)
- x = −8 and x = 2
- No solution
x − 3 = 5 or x − 3 = −5.
2. How many solutions does |x + 4| = −2 have?
- 0 (correct)
- 1
- 2
- Infinitely many
An absolute value cannot be negative.
3. Which describes |x − 1| < 4?
- x < 5
- −3 < x < 5 (correct)
- x < −3 or x > 5
- −5 < x < 3
Within 4 of 1.
Frequently asked questions
Is absolute value on the LCAT?
LUMS’s official LCAT guidelines list absolute value equations under Advanced Mathematics.
Why do absolute value equations have two answers?
Because two numbers are the same distance from a point: one on each side.
Can an absolute value equation have no solution?
Yes, when it is set equal to a negative number.