Absolute Value Inequalities

Front

What is absolute value?

Back

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

Front

How do you isolate the absolute value in an inequality?

Back

To isolate the absolute value, you may need to add or subtract terms from both sides of the inequality.

Front

What does the inequality |x| < a represent?

Back

It represents the values of x that are within a distance a from 0, resulting in the compound inequality -a < x < a.

Front

What does the inequality |x| > a represent?

Back

It represents the values of x that are more than a distance a from 0, resulting in the compound inequality x < -a or x > a.

Front

What is the first step in solving |x - 3| < 5?

Back

The first step is to set up the compound inequality: -5 < x - 3 < 5.

Front

How do you graph the solution of |x| < 3?

Back

You graph the interval (-3, 3) on a number line, using open circles to indicate that -3 and 3 are not included.

Front

What is the solution to the inequality |x + 2| > 4?

Back

The solution is x < -6 or x > 2.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often connected by 'and' or 'or', to describe a range of values.

Front

How do you solve the inequality -2|x| + 6 < 0?

Back

First, isolate the absolute value: |x| > 3, leading to x < -3 or x > 3.

Front

What is the significance of the 'or' in absolute value inequalities?

Back

The 'or' indicates that the solution can satisfy either of the inequalities, representing two separate ranges of values.