Solving 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 inequality |10 + 4x| < 14 represent?

Back

It represents the values of x for which the expression 10 + 4x is within 14 units of 0.

Front

Solve the inequality |10 + 4x| < 14.

Back

x < 1 and x > -6.

Front

What does the inequality -5|x - 4| > -20 imply?

Back

It implies that the expression |x - 4| must be less than 4.

Front

Solve the inequality -5|x - 4| > -20.

Back

x < 8 and x > 0.

Front

What does the inequality |3x - 9| < 3 mean?

Back

It means that the expression 3x - 9 is within 3 units of 0.

Front

Solve the inequality |3x - 9| < 3.

Back

2 < x < 4.

Front

What does the inequality |x + 3| > -8 indicate?

Back

Since absolute values are always non-negative, this inequality is true for all real numbers.