Absolute Value Equations and Inequalities

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, |-5| = 5 and |5| = 5.

Front

How do you solve an absolute value equation like |x| = a?

Back

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

Front

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

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given number. For example, |x| = -3 has no solution.

Front

What is the solution to the equation |-6x| = 30?

Back

The solutions are x = 5 and x = -5.

Front

Evaluate: |-12|

Back

12

Front

What is the first step to solve the inequality 6 - 2|m - 3| > -4?

Back

First, isolate the absolute value by adding 2|m - 3| to both sides: 6 > 2|m - 3| - 4.

Front

What does the inequality |x + 4| - 8 > 2 represent?

Back

It represents the values of x that are more than 2 units away from -4.

Front

How do you express the solution to |x| < a?

Back

The solution is -a < x < a.

Front

What is the solution to the equation 8|-2x + 4| = 96?

Back

The solutions are x = -4 and x = 8.

Front

What does the expression |x| mean?

Back

|x| means the absolute value of x, which is the non-negative value of x.