Absolute Value Inequalities

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

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 a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.

Front

Solve: |x - 5| < 3

Back

2 < x < 8.

Front

Solve: |2x + 1| ≥ 5

Back

x ≤ -3 or x ≥ 2.

Front

What is the solution set for |x + 4| - 8 > 2?

Back

x > 6 or x < -14.

Front

How do you graph the solution of |x| < a?

Back

You graph a number line with open circles at -a and a, shading the region between them.