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, isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case.

Front

What does |x - a| = b represent?

Back

This equation means that the distance between x and a is b units. It has two solutions: x = a + b and x = a - b.

Front

What is the first step in solving |x + 4| + 6 = 16?

Back

Isolate the absolute value by subtracting 6 from both sides to get |x + 4| = 10.

Front

Solve: |x - 2| - 12 = 8

Back

x = 22 or x = -18.

Front

Solve: |x + 6| = 10

Back

x = 4 or x = -16.

Front

Solve: |x + 8| − 5 = 2

Back

x = −1 or x = −15.

Front

Solve: 0.5|x − 9| + 10 = 4

Back

no solution.

Front

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

Back

The solution set is {0}.

Front

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

Back

It means that there are no values of x that can satisfy the equation, often because the absolute value cannot equal a negative number.