Free
Two-Step Equations
I can solve a two-step equation by undoing the operations in reverse order.
What students learn
Students learn to solve two-step equations, including negative coefficients and the variable on either side, by undoing the operations in reverse order, then checking the solution.
See inside
The key rule
To solve ax + b = c, undo in reverse order: first the adding or subtracting, then the multiplying. Do each move to both sides.
4x − 3 = 25 → 4x = 28 → x = 7
For x/a + b = c, the second move is to multiply both sides by a.
Watch out
Solve 5x + 15 = 40.
The mistake: x + 15 = 8, so x = −7The 5x and the 40 were divided by 5, but the 15 was not.
The fix: 5x = 25, so x = 5Subtract 15 first, then divide by 5. Check: 5(5) + 15 = 40.
The mistakes it targets
- Divides only some of the terms by the coefficient
- Undoes an operation with the same operation
- Gets the sign of a quotient wrong
- Divides when the variable is divided instead of multiplying
- Drops the minus sign in front of the x term
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 four 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, five 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.