Absolute Value Equations and 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 an absolute value equation?

Back

To solve an absolute value equation, isolate the absolute value expression and then split the equation into two separate cases, one for the positive and one for the negative.

Front

What does the inequality |x| < a represent?

Back

It represents the set of all numbers x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents the set of all numbers x that are more than a distance a from 0 on the number line.

Front

How do you graph the inequality |x| < a?

Back

You graph the interval (-a, a) on the number line, using open circles at -a and a.

Front

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

Back

You graph the regions x < -a and x > a on the number line, using open circles at -a and a.

Front

What is the first step in solving |v + 8| - 5 = 2?

Back

Get absolute value alone by adding 5 to both sides: |v + 8| = 7.

Front

What is the solution set for |v + 8| = 7?

Back

The solution set is v + 8 = 7 or v + 8 = -7, leading to v = -1 or v = -15.

Front

What is a compound inequality?

Back

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

Front

What does the compound inequality m < -1 OR m > 2 represent?

Back

It represents all values of m that are either less than -1 or greater than 2.