Absolute Value Inequalities

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 the inequality |x| < a?

Back

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

Front

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

Back

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

Front

What does the solution |p + 3| ≥ 10 represent?

Back

The solution represents the values of p that are either less than or equal to -13 or greater than or equal to 7.

Front

What is the solution to the inequality |x + 4| ≤ 8?

Back

The solution is -12 ≤ x ≤ 4.

Front

How do you interpret the solution x < 1 and x > -14?

Back

This means that x is between -14 and 1, not including the endpoints.

Front

What is the solution to the inequality |10 + 4x| < 14?

Back

The solution is -6 < x < 1.

Front

What does the inequality |3x - 7| < 11 imply about x?

Back

It implies that x is between -4/3 and 6.

Front

What is the graphical representation of |x| < a?

Back

The graph shows an open interval on the number line between -a and a.

Front

What is the graphical representation of |x| > a?

Back

The graph shows two open intervals: (-∞, -a) and (a, ∞).