Compound Inequalities: AND and OR
I can solve compound inequalities and graph AND and OR solution sets.
The problem this sheet solves
The connector is invisible in the working. Both halves look right all the way down the page, and only the final set and its graph reveal that the wrong one was chosen — so the grading advice here is to count pieces before reading numbers. Three degenerate cases are taught rather than avoided: 5
The key rule
Solve each part separately, then let the joining word build the answer. AND keeps only what both parts allow, giving at most one piece. OR keeps anything either part allows, giving two pieces. In a three-part chain, do every step to all three parts.
AND is the overlap. OR is everything covered. Check a number in the middle.
Watch out
The mistake: Reading 5 < x < 2 as a range and shading a piece between 2 and 5.
The fix: It asks for numbers above 5 AND below 2 at once, and no number does both. The answer is no solution.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.