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 always a non-negative value.

Front

How do you set up equations for |x + 1| = 4?

Back

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

Front

What does it mean if |x| = 0?

Back

It means that x must be 0, as the only number with an absolute value of 0 is 0 itself.

Front

What is the first step to solve |−2n| + 10 = −50?

Back

Recognize that the equation has no solution because the absolute value cannot be negative.

Front

What is the solution to |x - 3| = 0?

Back

The solution is x = 3.

Front

What happens when you have an absolute value equation equal to a negative number?

Back

There is no solution, as absolute values cannot be negative.

Front

How do you solve −2|−2r − 4| = -12?

Back

First, divide both sides by -2 to get |−2r − 4| = 6, then set up two equations: −2r − 4 = 6 and −2r − 4 = -6.

Front

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

Back

No solution, as absolute values cannot be negative.

Front

What is the process to solve |x| = a where a > 0?

Back

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

Front

What does the equation |x| = 5 represent?

Back

It represents two solutions: x = 5 and x = -5.