Absolute Value Equations

Front

What is the definition of absolute value?

Back

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

Front

What does the equation |x| = a imply when a > 0?

Back

It implies that x = a or x = -a.

Front

What does the equation |x| = 0 imply?

Back

It implies that x = 0.

Front

What is the solution to the equation |2x + 9| = 15?

Back

x = 3 and x = -12.

Front

What is the solution to the equation |x - 3| = 0?

Back

x = 3.

Front

What is the solution to the equation |x + 9| = -5?

Back

No solution, because absolute values cannot be negative.

Front

What is the solution to the equation |2x - 3| + 5 = 10?

Back

x = -1 and x = 4.

Front

What is the solution to the equation |x - 6| + 4 = 10?

Back

x = 12 and x = 0.

Front

How do you isolate the absolute value in an equation?

Back

Subtract or add constants from both sides of the equation to isolate the absolute value expression.

Front

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

Back

Set up two separate equations based on the definition of absolute value.