Compound Inequalities: AND and OR
I can solve compound inequalities and graph AND and OR solution sets.
What students learn
Students learn to solve a compound inequality, keep the overlap for AND and every number either part allows for OR, graph it as one piece or two rays, and test a number.
See inside
The key rule
Solve each part. AND keeps the numbers that make both parts true; OR keeps the numbers that make either part true. In a chain, do every step to all three parts.
2 < x + 1 < 5 → 1 < x < 4
Divide a chain by a negative and reverse each symbol: −2 < −x < 3 becomes 2 > x > −3.
Watch out
Describe the solution set of 5 < x < 2.
The mistake: the numbers between 2 and 5It reads the chain as a range, but the bigger number is on the left.
The fix: x > 5 and x < 2: no number does both, so no solutionTest 3: 5 < 3 is false. Every number fails one of the two parts.
The mistakes it targets
- Reads a chain as a range when its bigger number is on the left
- Turns an OR inequality into a between
- Does a step to the middle part of a chain only
- Divides a chain by a negative without reversing both symbols
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: two word problems and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.