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, you separate it into two inequalities: -a < x < a.

Front

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

Back

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

Front

What does the inequality |y - 1| ≤ 6 represent?

Back

It represents all values of y that are within 6 units of 1 on the number line.

Front

Solve the inequality |y - 1| ≤ 6.

Back

-5 ≤ y ≤ 7.

Front

What does the inequality |c + 4| < 5 represent?

Back

It represents all values of c that are less than 5 units away from -4 on the number line.

Front

Solve the inequality |c + 4| < 5.

Back

-9 < c < 1.

Front

What is the first step in solving |y - 4| ≥ 8?

Back

Separate into two inequalities: y - 4 ≤ -8 or y - 4 ≥ 8.

Front

Solve the inequality |y - 4| ≥ 8.

Back

y ≤ -4 or y ≥ 12.

Front

What does the inequality | -8x | < 8 represent?

Back

It represents all values of x that are less than 1 unit away from 0 when multiplied by -8.