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 a: |2a - 10| = 6

Back

a = 8, a = 2

Front

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

Back

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

Front

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

Back

k = -6, k = 12

Front

What is the first step in solving |x + 3| = 5?

Back

Set up two equations: x + 3 = 5 and x + 3 = -5.

Front

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

Back

r = 9/5, r = 0

Front

What is the solution set for |v + 8| - 5 = 2?

Back

{-1, -15}

Front

How do you check your solution for an absolute value equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

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

Back

a = 8, a = 2