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 by |x|.

Front

What does |x + 9| = -5 imply?

Back

This equation has no solution because absolute values cannot be negative.

Front

Solve for x: |5x| = 40.

Back

x = 8 and x = -8.

Front

What is the solution to |2x + 9| = 15?

Back

x = 3 and x = -12.

Front

How do you solve |x - 3| = 0?

Back

The solution is x = 3.

Front

What is the first step to solve |x - 6| + 4 = 10?

Back

Subtract 4 from both sides to get |x - 6| = 6.

Front

What are the two cases to consider when solving |x - 6| = 6?

Back

Case 1: x - 6 = 6; Case 2: x - 6 = -6.

Front

What is the solution to |x - 6| = 6?

Back

x = 12 and x = 0.

Front

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

Back

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 x that can satisfy the equation.