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 as |x|.

Front

Solve: |x - 2| - 12 = 8

Back

x = 22 or x = -18

Front

Solve: |x| = 4

Back

x = 4 or x = -4

Front

What does it mean if |x| = -k for any positive k?

Back

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

Front

Solve: 5|x| - 8 = 2

Back

x = 2 or x = -2

Front

Solve: |5x| = -20

Back

no solution

Front

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

Back

Isolate the absolute value expression on one side of the equation.

Front

Solve: 7|x - 9| - 5 = -3|x - 9| + 25

Back

x = 6 or x = 12

Front

What are the two cases to consider when solving |x - a| = b?

Back

Case 1: x - a = b; Case 2: x - a = -b.

Front

If |x| = a, what are the possible values of x?

Back

x = a or x = -a.