6.3 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

What does |x| = a imply when a < 0?

Back

It implies 'no solution' because absolute values cannot be negative.

Front

How do you solve |x| = a when a >= 0?

Back

Set up two equations: x = a and x = -a.

Front

What is the first step to solve |x + 2| = 4?

Back

Set up two equations: x + 2 = 4 and x + 2 = -4.

Front

What is the solution to |x - 3| = 5?

Back

x = 8 or x = -2.

Front

What does the equation |2x - 1| = -5 indicate?

Back

It indicates 'no solution' because absolute values cannot be negative.

Front

What is the first step to solve |x + 3| + 2 = 5?

Back

Subtract 2 from both sides to get |x + 3| = 3.

Front

How do you solve |−2n| + 10 = −50?

Back

It has 'no solution' because the left side cannot equal a negative number.

Front

What is the first step to solve -2|x + 3| = -10?

Back

Divide by -2 on both sides to get |x + 3| = 5.

Front

What are the two equations set up from |x + 2| = 4?

Back

x + 2 = 4 and x + 2 = -4.