Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple 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 at the same time.

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

What is the solution to the compound inequality x < 1 and x > 5?

Back

There is no solution because no number can be both less than 1 and greater than 5 at the same time.

Front

How do you graph the compound inequality x ≥ -2 and x > 3?

Back

On a number line, shade to the right from -2 (including -2) and shade to the right from 3 (not including 3).

Front

What is the solution to the compound inequality -3(2x + 1) < -15 or 1 - x ≥ 5?

Back

The solution is x ≤ -4 or x > 2.

Front

How do you write an inequality for the graph that shows -2 ≤ x ≤ 5?

Back

The inequality is -2 ≤ x ≤ 5.

Front

What is the solution to the compound inequality 2 < 3x - 12 < 5?

Back

Front

What does it mean if a compound inequality has no solution?

Back

It means that there is no value that satisfies all parts of the inequality.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, isolate the variable in each part of the inequality and find the intersection or union of the solutions.