Absolute Value Inequality Review

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 as |x|.

Front

How do you solve an absolute value inequality of the form |x| < a?

Back

To solve |x| < a, you split it into two inequalities: -a < x < a.

Front

How do you solve an absolute value inequality of the form |x| > a?

Back

To solve |x| > a, you split it into two inequalities: x < -a or x > a.

Front

What is the first step in solving the inequality |x - 4| - 3 < 5?

Back

The first step is to isolate the absolute value expression: |x - 4| < 8.

Front

What is the solution to the inequality |x + 5| < 9?

Back

The solution is -14 < x < 4.

Front

What does the inequality -4|x + 1| < -20 imply about the values of x?

Back

This inequality has no solution because the left side is always non-positive, while the right side is negative.

Front

How do you interpret the solution x < -6 or x > 4 in the context of absolute value inequalities?

Back

This means that the values of x are either less than -6 or greater than 4, indicating the distance from -1 is greater than 5.

Front

What is the solution to the inequality 4|x - 1| < 24?

Back

The solution is -5 < x < 7.

Front

How do you graph the solution of an absolute value inequality?

Back

You graph the critical points on a number line and shade the appropriate regions based on the inequality.

Front

What is the significance of the critical points in absolute value inequalities?

Back

Critical points are the values where the expression inside the absolute value equals zero or where the inequality changes direction.