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, you set up two separate equations: one for the positive case and one for the negative case.

Front

Solve the equation: |v + 8| − 5 = 2

Back

{−1, −15}

Front

Solve the equation: |−4 + 5x| = 16

Back

{−12/5, 4}

Front

Solve the equation: |2x – 3| + 5 = 10

Back

{−1, 4}

Front

Solve the equation: 3|−8x| + 8 = 80

Back

{−3, 3}

Front

Solve the equation: |2x + 9| = 15

Back

x = 3, x = −12

Front

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

Back

It means that there are no values for the variable that can satisfy the equation.

Front

What is the first step in solving |x| = a where a > 0?

Back

Set up two equations: x = a and x = -a.

Front

What is the solution set for |x| = 0?

Back

The solution set is {0}.