Solving 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 for k: |6 - 2k| = 18

Back

k = -6, k = 12

Front

What is the absolute value of |-26|?

Back

26

Front

Solve for r: −2|−2r − 4| = -12

Back

r = -5, r = 1

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 for r: 8 - 9|10r - 9| = -73

Back

r = 9/5, r = 0

Front

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

Back

It means that the expression inside the absolute value cannot equal the given value, indicating a contradiction.

Front

Solve for x: 8|-2x + 4| = 96

Back

x = -4, x = 8

Front

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

Back

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

Front

If |x| = 0, what is the value of x?

Back

x = 0.