➕ Algebra 1 · Equations
Solving Multi-Step Equations cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The plan (Dancing Cats Undo Chaos)
- 1. Distribute (every term, with its sign)
- 2. Combine like terms
- 3. Undo + or − on both sides, then × or ÷ on both sides
- 4. Check in the original equation
Tidy rules
- a(b + c) = ab + ac
- −(b + c) = −b − c
- −2(x − 5) = −2x + 10
- Plain numbers combine only with plain numbers
Fractions
- Clear them: multiply every term by the LCD
- x/2 + x/3 = 10 becomes 3x + 2x = 60
- A fraction times a group: multiply by the reciprocal
Worked example
- 3(x + 2) + 2x = 31
- 5x + 6 = 31 (tidy)
- 5x = 25 (subtract 6)
- x = 5 (divide by 5)
Watch out
- Distribute to every term
- Minus before parentheses flips every sign
- Tidying is one side at a time; undoing is both sides
Formulas
- Distributive property: a(b + c) = ab + ac and a(b − c) = ab − ac
- Minus before parentheses: −(b + c) = −b − c and −(b − c) = −b + c
- Reciprocal: (p/q) · (q/p) = 1 (when p ≠ 0 and q ≠ 0)
Solving Multi-Step Equations cheat sheet from HighSchoolQ.com, for personal study use.