Solving Linear Equations — Quick Reference Cheatsheet
A focused companion to the main Solving Linear Equations topic page on ACT Math.
ACT Math Elementary Algebra One-page reference
This is a one-page reference for Solving Linear Equations on the ACT math section. Use inverse operations to isolate the variable and verify the solution. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Solving Linear Equations topic page.
What this topic is
A Solving Linear Equations question tests basic algebraic manipulation — solving linear equations, factoring simple quadratics, and combining like terms. The ACT expects this to be automatic.
Core formulas you must memorise
- Distributive: a(b+c) = ab + ac
- Combine like terms: 3x + 2x = 5x
- Solve: isolate x using inverse operations
- Factor: x² + (p+q)x + pq = (x+p)(x+q)
- Difference of squares
If any of these formulas are not yet automatic, drill them via the Elementary Algebra formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
ACT questions on Solving Linear Equations typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Solving Linear Equations is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
Plug your answer back into the ORIGINAL equation, not your simplified version, to catch sign errors.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Solving Linear Equations questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Solving Linear Equations strategy guide. For category-wide context, browse all Elementary Algebra topics. For score-targeted study plans, see the score-band guides.