Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the equation |x| = a?

Back

Set up two equations: x = a and x = -a, then solve for x.

Front

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

Back

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

Front

Solve the equation |v + 8| − 5 = 2.

Back

v = -1 or v = -15.

Front

What is the solution to the equation 4|m| = -20?

Back

No solution, because absolute values cannot be negative.

Front

Solve the equation |2x + 9| = 15.

Back

x = 3 or x = -12.

Front

What are the two possible solutions for |x - 3| = 40?

Back

x = 43 or x = -37.

Front

What happens when you have a negative absolute value equation like -|−2r − 1| = 11?

Back

No solution, because absolute values are always non-negative.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

What does the expression |x| represent?

Back

The distance of x from 0 on the number line.