Solving 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 |A| = B, you set up two equations: A = B and A = -B.

Front

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

Back

k = -6, k = 12

Front

Solve for a: |2a - 10| = 6

Back

a = 8, a = 2

Front

What does it mean if |x - 3| = 0?

Back

It means that x = 3, as the absolute value is zero only when the expression inside is zero.

Front

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

Back

r = 9/5, r = 0

Front

What is the solution set for |x - 3| = 0?

Back

The solution set is {3}.

Front

Solve for r: −2|−2r − 4| = -12

Back

The solution set is {-5, 1}.

Front

What is the first step in solving |x| = a where a > 0?

Back

Set up two equations: x = a and x = -a.

Front

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

Back

It means that there are no values of the variable that can satisfy the equation.