Absolute Value

High School

Definition

When a negative number is made positive. In other words, absolute values depicts the distance between the number and the origin. For 0 and numbers that are already positive, there is no need to do anything to them in order to get their absolute values.

Worked examples

\(|{-7}| = 7 \quad |7| = 7 \quad |0| = 0\)
Absolute value gives the distance from zero, so negative numbers become positive and positive numbers stay the same.
\(|3 - 10| = |{-7}| = 7\)
Evaluate the expression inside the bars first, then take the absolute value of the result.

Common mistakes

  • \(|{-7}| = -7\) → \(|{-7}| = 7\) Absolute value is always zero or positive, never negative.
  • \(|a + b| = |a| + |b|\) → \(|a + b| \le |a| + |b|\) The equality holds only when a and b have the same sign; otherwise the left side is smaller.
  • \(|x| = 5 \)→\( x = 5\) → \(x = 5 \) or \( x = -5\) Both 5 and -5 are five units from zero, so absolute-value equations have two solutions.

Where you'll use it next

You'll use absolute value to solve absolute-value equations and inequalities, graph V-shaped absolute-value functions, measure distance on number lines, and represent error or magnitude in algebra, precalculus, and calculus.

Found in 5 StudyPug lessons

Absolute Value Function and Graph

Grade 11 Math

See how the absolute value function turns into a V-shaped graph, how to write it piecewise, and how to shift, stretch, and flip it.

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Angle and Absolute Value of a Complex Number

Grade 12 Math

Discover how to plot a complex number, measure its distance from the origin (modulus), and find the angle it makes with the real axis (argument).

12th Grade12th
Introduction to Absolute Value

Algebra

Discover what absolute value really means, how the absolute value bars work, and how to find the absolute value of any number quickly.

KindergartenKindergarten
Solving Absolute Value Equations

Grade 11 Math

A step-by-step guide to solving absolute value equations, including the two-case method, extraneous solution checks, and worked examples.

11th Grade11th
Mastering Absolute Value Inequalities: A Comprehensive Guide

Grade 11 Math

Unlock the secrets of absolute value inequalities with our step-by-step approach. Learn to solve, graph, and apply these crucial math concepts to real-world problems. Elevate your algebra skills today!

11th Grade11th

See also

Absolute Value RulesAbsolute Value of a Complex NumberAdditive inverse of a numberMagnitude of a VectorRadical

Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026

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