Solving Absolute Value Equations

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value.

Front

Why is absolute value always written as a positive?

Back

Absolute value is talking about distance, and distance is always measured by positive numbers.

Front

Solve the equation: |x + 7| = 12

Back

x = 5 or x = -19.

Front

Evaluate the expression: |5 + 4|

Back

9.

Front

Solve the equation: |v + 8| − 5 = 2

Back

v = -1 or v = -15.

Front

What does the equation -|−2r − 1| = 11 imply?

Back

No Solution, because absolute values cannot be negative.

Front

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

Back

x = a or x = -a.

Front

What is the geometric interpretation of absolute value?

Back

It represents the distance from a point to the origin on a number line.

Front

How do you solve an absolute value equation?

Back

Isolate the absolute value expression, then set up two separate equations: one for the positive case and one for the negative case.

Front

What is the solution set for |x| < a?

Back

-a < x < a.