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 always a non-negative value.

Front

Solve for t: |t - 8| + 4 = 11

Back

t = 1 or t = 15

Front

How many solutions does the equation |-6v| - 4 = -4 have?

Back

One solution.

Front

How many solutions does the equation 4|m| = -20 have?

Back

No solution.

Front

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

Back

It means that there are no values that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

Solve for v: -4 = |-6v| - 4

Back

v = -1/3 or v = 1/3.

Front

How do you isolate the absolute value in an equation?

Back

You can isolate the absolute value by moving all other terms to the opposite side of the equation.

Front

What is the first step to solve |x + 3| = 5?

Back

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

Front

What is the solution to the equation 0 = -6|9v - 7|?

Back

One solution.

Front

Why is absolute value always positive?

Back

Absolute value represents distance, and distance is always measured as a positive quantity.