Compound and Absolute Value Inequalities Review

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

What does the inequality |x| < a represent?

Back

It represents the set of all x values that are within a distance a from 0, which can be expressed as -a < x < a.

Front

What does the inequality |x| > a represent?

Back

It represents the set of all x values that are more than a distance a from 0, which can be expressed as x < -a or x > a.

Front

What is the solution to the inequality |2x + 6| < 0?

Back

No solution, because absolute values are always non-negative.

Front

How do you solve the inequality -8 < 2(x + 4)?

Back

First, simplify to get -8 < 2x + 8, then subtract 8 from both sides to get -16 < 2x, and finally divide by 2 to find x > -8.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

x > -9, after simplifying the inequality.

Front

What does the term 'compound inequality' mean?

Back

A compound inequality combines two or more 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 simultaneously, while 'or' means at least one of the conditions must be true.

Front

How do you graph the solution of an inequality?

Back

You represent the solution on a number line, using open circles for non-inclusive boundaries and closed circles for inclusive boundaries.

Front

What is the solution set for the compound inequality x < -8 or x < 2?

Back

The solution set includes all x values less than -8 and all x values less than 2.