Absolute Value
Definition
Worked examples
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
Found in 5 StudyPug lessons
Grade 11 Math
Absolute value is basically the distance between "number" and "zero" on a number line. We will look into this concept in this lesson. We will also learn how to express absolute value functions as piecewise functions.
Grade 12 Math
There are times when we are interested in obtaining a better understanding of the properties of a complex number, such as its argument and modulus. In this section, we will learn how to calculate the argument, also known as the angle, and the modulus, also known as the magnitude or the absolute value, of a complex number.
Grade 11 Math
An absolute value or modulus of a real number is always positive. Therefore, when solving absolute value equations, we need to establish two cases for each equation. One case is to set the quantity inside the absolute value notation as positive; whereas another case is to set the value as negative.
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!
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026