What is Absolute Value?
Absolute value measures the distance of a number from zero on the number line, ignoring its sign. It's written |x| and the result is always non-negative, whether x starts positive or negative.
The absolute value of x, written |x|, equals x if x is positive or zero, and −x if x is negative — it's always the non-negative distance from zero.
Try it: interactive calculator
Step-by-step worked examples
Find |−9|.
−9 is negative, so |−9| = −(−9) |−9| = 9
Solve |x − 3| = 5.
x − 3 = 5 or x − 3 = −5 x = 8 or x = −2
Simplify |4| − |−6|.
|4| = 4, |−6| = 6 4 − 6 = −2
Flashcards
Quick quiz
Q1.What is |−12|?
Q2.Solve |x| = 7.
Q3.What is |3 − 8|?
Q4.Which is true for all real x?
The full card deck, worked steps and AI-tutor support for “What is Absolute Value?” are in Notek — study by hand before your exam.
Common mistakes
Assuming |x| always equals x. — Correct: |x| = x only when x ≥ 0; if x is negative, |x| = −x.
Solving |x| = −5 for x. — Correct: Absolute value can't equal a negative number — this equation has no solution.
Dropping the bars mid-calculation: |x−3| turns into x−3 automatically. — Correct: Evaluate what's inside first, or split into both cases before removing the bars.
Thinking |−x| = −x. — Correct: |−x| = |x|, which is a positive value (or zero).
FAQ
What is the formula for absolute value?
|x| = x when x ≥ 0, and |x| = −x when x < 0 — the result is always non-negative.
How do you calculate absolute value?
Drop the sign: if the number is negative, flip it positive; if it's positive or zero, leave it as is.
What are examples of absolute value?
|5| = 5, |−5| = 5, and |0| = 0.
Why is absolute value never negative?
It represents distance, and distance can't be negative — it measures how far a number is from zero.