Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is 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

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does it mean if |x| = -a?

Back

If |x| = -a, where a is a positive number, there is no solution because absolute values cannot be negative.

Front

Solve the equation |2a - 10| = 6.

Back

a = 8 or a = 2.

Front

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

Back

x = 3 or x = -12.

Front

What is the solution to |6 - 2f| = -5?

Back

No solution, because absolute values cannot be negative.

Front

Solve the equation |−4 + 5x| = 16.

Back

x = 4 or x = -5.

Front

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

Back

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

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

What is the general form of an absolute value equation?

Back

The general form is |Ax + B| = C, where A, B, and C are constants.