Solve Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the equation |x| = a?

Back

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

Front

What does it mean if |x| = -a?

Back

If |x| = -a, there is no solution because absolute values cannot be negative.

Front

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

Back

x = 3, x = -12

Front

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

Back

a = -8, a = -2

Front

What is the first step in solving |−2n| + 10 = −50?

Back

Recognize that |−2n| + 10 cannot equal a negative number, so there is no solution.

Front

Solve the equation: |v + 8| − 5 = 2

Back

v = -1, v = -15

Front

What is the solution to the equation −2|−2r − 4| = −12?

Back

r = -5, r = 1

Front

What is the significance of the absolute value symbol?

Back

The absolute value symbol indicates the non-negative distance of a number from zero.

Front

How do you graph an absolute value function?

Back

An absolute value function graphs as a V-shape, opening upwards if the coefficient is positive.