12-14-23 Absolute Value Inequalities (Greater Than)

Front

What is an absolute value inequality?

Back

An inequality that contains an absolute value expression, indicating the distance of a number from zero on the number line.

Front

How do you isolate the absolute value in an inequality?

Back

You can isolate the absolute value by performing operations such as addition, subtraction, multiplication, or division on both sides of the inequality.

Front

What does |x| > a mean?

Back

It means that x is either greater than a or less than -a.

Front

What is the first step to solve |x + 4| + 8 > 2?

Back

Get the absolute value alone by subtracting 8 from both sides.

Front

Solve the inequality |x - 3| > 5.

Back

x < -2 or x > 8.

Front

What is the solution set for |x + 4| + 8 > 2?

Back

All real numbers.

Front

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

Back

You plot the critical points and shade the regions that satisfy the inequality.

Front

What does the inequality |3x + 9| > 27 represent graphically?

Back

It represents two rays extending from the critical points where the expression equals 27.

Front

What is the critical point in the inequality |6x + 9| > 15?

Back

The critical points are x = -4 and x = 1.

Front

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

Back

Substitute values from the solution set back into the original inequality to verify.