Absolute Value Equations

Front

What is an absolute value equation?

Back

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 an absolute value equation?

Back

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

Front

What does |x| = a mean?

Back

It means x can be either a or -a, provided a is non-negative.

Front

What is the first step in solving |x + 2| = 4?

Back

Set up two equations: x + 2 = 4 and x + 2 = -4.

Front

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

Back

x = 3.

Front

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

Back

There is no solution, because absolute values cannot be negative.

Front

What is the first step to solve |2x - 1| = -5?

Back

Recognize that there is no solution, since absolute values cannot equal a negative number.

Front

How do you interpret |x + 1| = 4?

Back

It means x + 1 can be 4 or -4.

Front

What is the solution set for |x| = 5?

Back

x = 5 or x = -5.

Front

What happens when you have an absolute value equation equal to zero?

Back

The expression inside the absolute value must equal zero.