Definition: Equations with absolute value

An equation with absolute value includes an expression within absolute value bars, such as \$|x|\$. The absolute value of a number is its distance from zero on the number line, regardless of direction, so it is always non-negative.

Explanation:

The image shows how to solve the absolute value equation \$ \∣x − 15\∣ = 12 \$ by splitting it into two cases:
1.Positive Case:
x - 15 = 12
Solve for x:
x = 27

2.Negative Case:
x - 15 = -12
Solve for x:
x = 3 Both solutions, x = 27 and x = 3 are verified to satisfy the original equation \$ \∣x − 15\∣ = 12 \$.