Math Practice Online > free > lessons > Florida > 9th grade > Absolute Value Equations

Here are some tips for Absolute Value Equations, which aligns with Florida state standards:

Absolute Value Equation

You must understand absolute values and inequalities to master this topic.
To review absolute value, see Absolute Value 1 and Absolute Value 2.
To review the Single Variable Inequalities topic, see here.

 Where A is the expression between the absolute value signs and b is a positive number, • when solving an equation with the form | A| = b, solve A = b   or   A = - b • when solving an equality with the form | A| < b, solve - b < A < b This rule is also true for ≤. • when solving an equality with the form | A| > b, solve A < - b   or   A > b This rule is also true for ≥.

Example 1: Equations

Solve for x.

1.  |x| = 5

Following the rules above, we get x = 5 or x = -5.

2.  |x| = -1
By definition of absolute value, |x| is always positive. So there is no x value that will work in this equation.

3.  |x - 6| = 4
 x - 6 = 4 or x - 6 = -4 x - 6 + 6 = 4 + 6 x - 6 + 6 = -4 + 6 x = 10 x = 2

Example 2: Inequalities

Solve for x.

1.  |x| ≥ 5

Following the rules above, we get x ≥ 5 or x ≤ -5.