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Adam's Alphabet

A free Grades 6–8 math library — clear lessons, hand-picked video walkthroughs, printable worksheets, and quizzes. Built by a student tutor for students who learn differently.

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αAπΣ∞∂θ√x²≠∫÷≤%+−½αβΔλφ³≈∑°
  1. Home/
  2. Mathematics/
  3. Grade 6/
  4. Unit 4/
  5. Inequalities & Number Lines
Grade 6 · Unit 4Topic 2 of 3~14 min

Inequalities & Number Lines

Solve like equations, then graph every value that works.

All topics in this unit
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 1 · Learn

Walkthrough

Read this first — it covers the idea in plain language with a worked example.

Reading inequality symbols

An inequality compares values that are not necessarily equal: < (less than), > (greater than), ≤ (at most), ≥ (at least). "At most 9" means x ≤ 9; "fewer than 5" means x < 5.

Solving and graphing

Solve an inequality the same way you solve an equation. Then graph the solution on a number line: an open circle for < or >, a closed (filled) circle for ≤ or ≥.

Worked example

Solve and graph x + 3 < 10

  1. →Subtract 3 from both sides: x < 7.
  2. →Graph an open circle at 7 and shade everything to the left.

Watch out

If you multiply or divide both sides by a negative number, flip the inequality sign.

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 2 · Watch

Video walkthrough

Watch the main video, then check the second take if you want another explanation.

Khan Academy

Intro to Inequalities

Symbols like < and ≥ and what they mean on a number line.

Watch on YouTube
Math Antics

Solving Inequalities

Solve inequality problems the same way you solve equations.

Watch on YouTube
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 3 · Practice

Practice

Try a worksheet or work through some problems before the quiz.

Khan Academy

Equations & inequalities practice

Open resource
πΣ√≠≤+αβΔπΣx²θ÷+
Step 4 · Check

Quick check

A couple of questions to make sure this topic stuck. Retake as many times as you want.

Inequalities & Number Lines

Question 1 of 3

Medium

Which inequality represents 'x is at most 9'?

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
←Previous · Topic 1 of 3One-Step Equations→Next up · Topic 3 of 3Independent & Dependent Variables