Multi-Step Inequalities and the Reversal Rule
I can solve multi-step inequalities and reverse the symbol only when I multiply or divide by a negative.
What students learn
Students learn to solve multi-step inequalities, reverse the symbol only when they multiply or divide both sides by a negative number, and test a number from their answer.
See inside
The key rule
Solve as you would an equation. When you multiply or divide both sides by a negative number, reverse the symbol; adding or subtracting never reverses it.
−2x > 8 → x < −4
Test a number from your answer in the first inequality: a missed reversal fails at once.
Watch out
Solve 6x − 1 < −19.
The mistake: 6x < −18, so x > −3It reverses the symbol, but 6 is positive.
The fix: 6x < −18, so x < −3Divide by positive 6: the symbol stays. Test −4: −25 < −19.
The mistakes it targets
- Divides by a negative and keeps the inequality symbol
- Reverses the symbol just because a number is negative
- Gets a sign wrong when distributing a negative
- Gives an excluded boundary as the greatest integer solution
The interactive Teacher Deck (33 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 (five 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.