12-18-24 Absolute Value Inequalities (Greater Than)

Front

What is an absolute value inequality?

Back

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

Front

How do you solve an absolute value inequality of the form |A| > B?

Back

To solve |A| > B, split the inequality into two cases: A > B or A < -B.

Front

What is the first step in solving |6x + 9| > 15?

Back

Get absolute value alone by dividing by 1 (if necessary) and then split into two equations.

Front

Solve the inequality |2x + 5| > 3.

Back

x < -4 or x > -1.

Front

What does the solution x < -4 or x > -1 represent?

Back

It represents the values of x that are either less than -4 or greater than -1, indicating two separate ranges on the number line.

Front

Solve the inequality |3x - 2| > 7.

Back

x < -1 or x > 3.

Front

What is the significance of the solution x < -1 or x > 3?

Back

It indicates that the expression 3x - 2 is either greater than 7 or less than -7.

Front

Determine the values of x that satisfy |12x - 6| > 30.

Back

x < -2 or x > 3.

Front

What is the general approach to graphing the solution of an absolute value inequality?

Back

Graph the critical points on a number line and shade the regions that satisfy the inequality.

Front

What does the inequality |A| > B imply about A?

Back

It implies that A is either greater than B or less than -B.