Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

How do you solve the inequality |x| < a?

Back

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

Front

How do you solve the inequality |x| > a?

Back

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

Front

What does the expression |x + 3| > 8 represent?

Back

It represents the values of x that are more than 8 units away from -3 on the number line.

Front

What is the solution to the inequality |x + 3| > 8?

Back

x > 5 or x < -11.

Front

How do you solve the equation |x - 4| = 7?

Back

To solve |x - 4| = 7, set up two equations: x - 4 = 7 and x - 4 = -7.

Front

What is the solution to the equation |x - 4| = 7?

Back

x = 11 or x = -3.

Front

What does the expression |2x - 1| = 7 represent?

Back

It represents the values of 2x - 1 that are exactly 7 units away from 0.

Front

What is the solution to the inequality -5|x - 4| > -20?

Back

x < 8 and x > 0.

Front

What is the first step in solving an absolute value inequality?

Back

Isolate the absolute value expression on one side of the inequality.