Solving Equations
One-step, two-step, and variables-on-both-sides equations, and equation word problems.
This page is a free outline of what the Solving Equations lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Equations – Special Cases (No / Infinite Solutions) Sometimes the variable cancels out as you solve: a false result like 5 = 9 means no solution, while a true one like 6 = 6 means every value works — infinitely many.
- One-Step Equations A one-step equation needs a single inverse operation to isolate the variable — for example, x − 38 = 17 is solved by adding 38 to both sides.
- Solving Equations with Variables on Both Sides
- Translating Words into Equations Turning a word problem’s sentences into an equation — “a number times 12, minus 20, is 100” becomes 12h − 20 = 100 — so you can solve for the unknown.
- Two-Step Equations
- Two-Variable Word Problems A word problem with two unknowns, captured as equations in x and y (often a system) instead of a single-variable equation.
- Word Problems – Linear Equations A word problem that translates into a single linear equation — a constant-rate situation you set up and solve for one unknown.
- Word Problems – Multi-Step A word problem that takes several operations or stages to reach the answer, so you break it into ordered steps rather than solving in one move.
Linked concepts (purple →) have a full explanation. Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, Solving Equations comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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