Multi-Step Equations
I can simplify an equation by distributing and combining like terms, then solve it.
The problem this sheet solves
The actual difficulty is preprocessing. Distribute across the parentheses, collect the like terms already sitting on their own side, and what remains is the two-step equation the student can already solve. The common failure is partial distribution, 3(x + 4) = 27 written as 3x + 4 = 27, which produces a different equation and a confidently wrong answer. This sheet is explicit that it adds a simplifying stage rather than a solving method, which is the framing that keeps students from collecting procedures. Distribution is treated as reaching every term inside, and each equation keeps its variable on one side so the new work is isolated to the part that is actually new.
The key rule
Simplify each side first, then solve. Distribute across every term inside the parentheses, combine the like terms that result, and what remains is a two-step equation you already know how to finish.
There is no new solving method on this page. The only new work happens before the solving starts.
Watch out
The mistake: Writing 3(x + 4) = 27 as 3x + 4 = 27.
The fix: The 3 multiplies everything inside, so the 4 becomes 12: 3x + 12 = 27. Leaving the second term alone makes it a different equation.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
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.