Absolute Value Inequalities
I can solve absolute value inequalities and graph the one-piece or two-piece answer.
What students learn
Students learn to get the absolute value alone, read less than as within (one piece) and greater than as beyond (two rays), read a negative right side exactly, and test a number.
See inside
The key rule
Get the absolute value alone. For b > 0, less than: the inside is between −b and b, one piece; greater than: the inside is less than −b or greater than b, two rays.
|u| < 5 → −5 < u < 5
If b is negative, read the symbol: < has no solution, > is all real numbers.
Watch out
Solve |x − 2| > 6.
The mistake: −6 < x − 2 < 6, so −4 < x < 8One piece is the answer to < 6, not to > 6.
The fix: x − 2 < −6 or x − 2 > 6, so x < −4 or x > 8More than 6 from 2 is two rays. Test 9: |9 − 2| = 7, and 7 > 6.
The mistakes it targets
- Solves a greater-than inequality as one piece, like a less-than
- Reads the center with the wrong sign
- Misreads an absolute value compared with a negative number
- Leaves the symbol unreversed on the negative side
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: one word problem, a reasoning prompt 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.