Solving Absolute-Value Equations

Front

What is an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an absolute-value equation?

Back

To solve an absolute-value equation |x| = a, you set up two equations: x = a and x = -a.

Front

Solve the equation: |2a − 10| = 6

Back

a = 8, a = 2

Front

Solve the equation: |2a + 10| = 6

Back

a = -8, a = -2

Front

What does it mean if an absolute-value equation has no solution?

Back

An absolute-value equation has no solution if the expression inside the absolute value cannot equal the given value (e.g., |x| = -5 has no solution).

Front

Solve the equation: |−2n| + 10 = −50

Back

No Solution

Front

What is the first step in solving an equation with absolute value?

Back

Isolate the absolute value expression on one side of the equation.

Front

Solve the equation: −2|−2r − 4| = −12

Back

r = -5, r = 1

Front

What happens when you multiply an absolute value by a negative number?

Back

Multiplying an absolute value by a negative number reverses the equation, so you must divide by the negative to isolate the absolute value.

Front

Solve the equation: 3|−8x| + 8 = 80

Back

x = -3, x = 3