Multi-Step Equations
I can simplify each side by distributing and combining like terms, then solve the equation.
What students learn
Students learn to solve multi-step equations: they distribute and combine like terms to simplify a side first, then undo the operations in reverse order and verify the solution.
See inside
The key rule
First simplify each side: distribute, then combine like terms. Then undo in reverse order: the adding or subtracting first.
4(x − 1) = 20 → 4x − 4 = 20 → x = 6
A negative in front multiplies every term inside, sign and all: −2(x − 5) = −2x + 10.
Watch out
Solve 2(x + 9) + x = 30.
The mistake: 2x + 9 + x = 30, so x = 7The 2 multiplied the x but not the 9.
The fix: 2x + 18 + x = 30, so x = 4The 2 multiplies both terms in the ( ). Then 3x = 12.
The mistakes it targets
- Multiplies only the first term inside the parentheses
- Loses the sign when the number in front of parentheses is negative
- Changes only the first sign after a minus in front of parentheses
- Drops the sign of a negative term when combining like terms
- Multiplies only the number term inside the parentheses
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 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.