Which statement best describes the key difference when solving compound inequalities involving 'and' versus 'or'?

With 'and', the solution must satisfy both inequalities; with 'or', the solution must satisfy at least one inequality.

Solve the compound inequality: 2 < x + 1 ≤ 5. Graph the solution set on a number line.

1 < x ≤ 4. The graph should show an open circle at 1, a closed circle at 4, and shading between them.

x > -2 or x < -2. The graph should show an open circle at -2, with shading to the left and to the right (excluding -2).

9th GradeMath50 min

I can solve compound inequalities and graph the solution sets on a number line.

19 min

5.4 Solving Compound Inequalities

Megan Tompkins

10 min

Key concepts students will learn:

•
A compound inequality consists of two inequalities considered together, which can be an intersection or a union.
•
An intersection uses the word and, meaning the solution must be true for both inequalities, representing where the graphs overlap.
•
A union uses the word or, meaning the solution must be true for at least one inequality, representing wherever the inequalities are shown on a graph.

15 min

6 questions • Multiple choice & Short answer

5 min

“Solve the compound inequality and graph the solution set on a number line: 2x < 6 or x + 1 > 5”

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