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 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 inequality |p + 3| ≥ 10 represent?

Back

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

Front

What is the solution to the inequality |3x + 6| ≥ 15?

Back

The solution is x ≤ -7 or x ≥ 3.

Front

What does the inequality |2x - 4| > 10 indicate?

Back

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

Front

How do you express |x + 4| ≤ 8 in interval notation?

Back

The solution in interval notation is [-12, 4].

Front

What is the graphical representation of |x| < 5?

Back

The graph shows an open interval from -5 to 5, excluding the endpoints.

Front

What is the difference between |x| < a and |x| ≤ a?

Back

|x| < a means x is strictly between -a and a, while |x| ≤ a includes the endpoints -a and a.

Front

What is the solution to the inequality |3x - 7| < 11?

Back

The solution is -4/3 < x < 6.