➕ Algebra 1 · Equations
Equations with Variables on Both Sides 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 (STAND)
- S: Simplify each side
- T: Take the variable terms to one side (both sides)
- A: Add or subtract the plain numbers (both sides)
- N: Now divide by the coefficient (not zero)
- D: Double-check in the original
Three outcomes
- An x is left: one solution, like x = 4
- x-terms vanish, true (7 = 7): infinitely many solutions
- x-terms vanish, false (7 = 9): no solution
Example
- 5x + 2 = 3x + 10
- 2x + 2 = 10 (subtract 3x)
- 2x = 8 (subtract 2)
- x = 4 (divide by 2)
Watch out
- Both sides, every time
- 5x and 3x on opposite sides do not add
- 0 = 0 does not mean x = 0
Formulas
- One solution: ax + b = cx + d with a ≠ c gives x = (d − b) ÷ (a − c)
- Infinitely many solutions: ax + b = ax + b is true for every x
- No solution: ax + b = ax + d with b ≠ d is never true
Equations with Variables on Both Sides cheat sheet from HighSchoolQ.com, for personal study use.