Solve 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 denoted as |x|.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case.

Front

What is the solution to |x| = a when a > 0?

Back

The solutions are x = a and x = -a.

Front

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

Back

It means that the expression inside the absolute value cannot equal the given value, often occurring when the absolute value is set equal to a negative number.

Front

Solve the equation |x - 3| = 5.

Back

x - 3 = 5 or x - 3 = -5; solutions are x = 8 and x = -2.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

Solve the equation |2x + 1| = 3.

Back

2x + 1 = 3 or 2x + 1 = -3; solutions are x = 1 and x = -2.

Front

What is the first step in solving |x + 4| = 6?

Back

Isolate the absolute value expression, then set up two equations: x + 4 = 6 and x + 4 = -6.

Front

If |x| = 0, what is x?

Back

x = 0.

Front

Solve the equation |x - 2| = 4.

Back

x - 2 = 4 or x - 2 = -4; solutions are x = 6 and x = -2.