Multistep, Compound, & 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

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' represents 'less than or equal to'.

Front

What is a compound inequality?

Back

A compound inequality is formed by combining two inequalities using the words 'and' or 'or'.

Front

What does 'AND' mean in a compound inequality?

Back

In a compound inequality, 'AND' means that both conditions must be true simultaneously.

Front

What does 'OR' mean in a compound inequality?

Back

In a compound inequality, 'OR' means that at least one of the conditions must be true.

Front

How do you graph the solution of an inequality?

Back

To graph the solution of an inequality, use a number line and shade the region that represents the solution set, using open or closed circles to indicate whether endpoints are included.

Front

What is the solution to the inequality 2w - 1 < 11?

Back

The solution is -5 < w < 6.

Front

How do you solve the inequality 3x + 2 < -4?

Back

First, subtract 2 from both sides to get 3x < -6, then divide by 3 to find x < -2.

Front

What is the solution to the inequality 4x + 4 > 24?

Back

First, subtract 4 from both sides to get 4x > 20, then divide by 4 to find x > 5.