Skill: absolute-value

Absolute Value Tutor Help

Stuck on absolute value? Review the core ideas, read answers to common questions, and send a question to a tutor.

1 Quick recap

Absolute value is distance from zero, so |x − a| = b splits into two cases (x − a = b or x − a = −b) — after you isolate the bars. Inequalities become distance statements: |x − a| < b is one interval, |x − a| > b is two rays.

Core ideas

Isolate the |…| expression first, then split into two cases.
|x − a| = b (b > 0) → x = a + b or x = a − b.
|x − a| < b → a − b < x < a + b (one interval).
|x − a| > b → x < a − b or x > a + b (two rays).
Negative right side on an equation: no solution. Always substitute back to check.

2 Questions students ask

The questions a tutor hears most about this skill.

Why do I get two answers?

Because distance works both ways: being 5 from 3 means x = 8 (5 to the right) or x = −2 (5 to the left). One case per direction.

Do I always divide first in 2|x + 1| = 10?

Yes — the two-case rule only applies when the absolute value stands alone. Isolate |x + 1| = 5 first, then split.

How do I remember which inequality gives “or”?

Greater-than means “far away”, and far away happens in two directions — that is the “or”. Less-than means “close”, which is one connected neighborhood.

3 Ask a tutor

Stuck on a problem? Send it in — a tutor will walk you through it.

Demo form: this contact form is a demonstration only — it does not send anywhere and has no backend connected. Nothing you type leaves this page.