Solving and Graphing 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

How do you graph the inequality x ≤ -2 OR x > 5?

Back

Graph a solid dot at -2 and shade to the left. Then graph an open dot at 5 and shade to the right.

Front

How do you graph the inequality -2 ≤ x < 5?

Back

Graph a solid dot at -2 and an open dot at 5, shading the region between them.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

You must flip the inequality sign when multiplying or dividing both sides by a negative number.

Front

Solve the compound inequality: -3 ≤ 2x - 1 ≤ 5.

Back

-1 ≤ x ≤ 3.

Front

Solve the compound inequality: 0 < x + 7 < 9.

Back

-7 < x < 2.

Front

What is the solution set for the inequality x < 3 AND x > -1?

Back

The solution set is all x such that -1 < x < 3.

Front

What is the solution set for the inequality x ≤ 4 OR x > 6?

Back

The solution set includes all x such that x ≤ 4 or x > 6.