Solving Compound Inequalities in College Algebra

What is a compound inequality?

• An equation with one variable

• An inequality with more than one part

• An equation with two variables

• A single inequality

In the inequality -5 < x + 13 <= 22, what is the first step to isolate x?

• Divide by 13

• Multiply by 13

• Subtract 13 from all parts

• Add 13 to both sides

What does the interval notation (-18, 9] represent?

• x is between -18 and 9, including both

• x is between -18 and 9, including 9

• x is between -18 and 9, including -18

• x is between -18 and 9, excluding both

In the inequality 17 <= 11 - 2x <= 35, what should you do after moving the 11?

• Multiply by -2

• Divide by -2

• Subtract 2 from all parts

• Add 2 to all parts

What happens to the inequality symbols when you divide by a negative number?

• They disappear

• They become equal signs

• They change direction

• They stay the same

Why is it important to rewrite the inequality in order from least to greatest?

• To make it easier to multiply

• To make it easier to solve

• To make it easier to add

• To make it easier to graph

In the rewritten inequality -12 <= x <= -3, what does the equal sign indicate?

• x is not included

• x is included

• x is greater than -12

• x is less than -3

What is the interval notation for the inequality -12 <= x <= -3?

• (-12, -3)

• [-12, -3]

• (-12, -3]

• [-12, -3)

When writing interval notation, what does a bracket indicate?

• The number is not included

• The number is included

• The number is less

• The number is greater

What is the final step in solving the inequality 17 <= 11 - 2x <= 35?

• Multiply by -2

• Divide by -2

• Subtract 11 from all parts

• Add 11 to all parts