Inequalities
Solving and graphing inequalities, the negative-flip rule, and compound inequalities.
This page is a free outline of what the Inequalities lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Compound Inequalities A compound inequality combines two conditions, like 12 < a < 18 (older than 12 and younger than 18) — describing values that fall between two bounds or satisfy either of two ranges.
- Flip Rule (Inequalities with Negatives) When you multiply or divide both sides of an inequality by a negative number, you flip the inequality sign — so −3x ≤ 12 becomes x ≥ −4.
- Graphing Inequalities on the Number Line Graphing an inequality shows its range on a number line: an open circle for < or > (endpoint not included), a closed circle for ≤ or ≥ (included), with an arrow toward all the solutions.
- One-Step Inequalities A one-step inequality is solved with a single inverse operation, just like a one-step equation — x + 5 < 8 gives x < 3 — but the answer is a range of values, not one number.
- Two-Step Inequalities A two-step inequality needs two inverse operations to isolate the variable, like 2x + 3 > 9 → x > 3 — solved like a two-step equation, with a range as the answer.
- Two-Variable Inequalities A two-variable inequality, like y > 2x + 1, describes a whole region of the coordinate plane — every point on one side of the boundary line — not just a single line.
- Writing Inequalities Writing an inequality turns a range described in words into symbols: “at least 70” becomes ≥ 70, “below 32” becomes < 32. The wording tells you which symbol to use.
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Inside the app, Inequalities 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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