Absolute Value Equations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by |x|.

Front

What does the equation |x| = a represent?

Back

It represents two equations: x = a and x = -a, where a is a non-negative number.

Front

What is the first step to solve |x + 1| = 4?

Back

Set up 2 equations: x + 1 = 4 and x + 1 = -4.

Front

What is the solution set for |x + 9| = -5?

Back

No solution, because absolute values cannot be negative.

Front

What is the first step to solve |2x - 1| = -5?

Back

No solution, because absolute values cannot be negative.

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 is the solution set for -2|−2r − 4| = -12?

Back

{-5, 1}.

Front

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

Back

It means that the equation cannot be satisfied because the absolute value cannot equal a negative number.

Front

How do you solve an absolute value equation with a negative coefficient?

Back

First, divide both sides by the negative coefficient to isolate the absolute value expression.

Front

What is the first step to solve |x - 3| = 7?

Back

Set up 2 equations: x - 3 = 7 and x - 3 = -7.