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Solving & Graphing Inequalities

Ninth graders learn to solve linear inequalities and graph the solutions on a number line — with a key twist: flipping the inequality sign when multiplying or dividing by a negative number.

Grade 9Inequalities55 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Solve linear inequalities.
  • ✓Graph solutions on a number line.
  • ✓Use open vs. closed circles.
  • ✓Flip the sign for a negative.
Essential Question

An inequality like x > 3 has infinitely many solutions, not just one. How do we solve inequalities — and show every answer on a number line?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

Graph the Inequality

Project this and set the boundary and inequality type. Watch the number line show open/closed circles and the shaded direction!

≤ Graph an inequality on a number lineTry it
Boundary: x = 2

The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Many Answers

5 min

x > 3 has infinitely many solutions — how do we show them all?

👩‍🏫 Teacher Moves

  • Show an inequality.
  • Ask how many solutions.
  • Set the goal: inequalities.

🎒 Student Actions

  • See the inequality.
  • Realize “many.”
  • Predict a graph.
2

I Do — Solve & Graph

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Solve like an equation.
  • Graph on a number line.
  • Open vs. closed circles.

🎒 Student Actions

  • Solve it.
  • Graph it.
  • Choose the circle.
3

We Do — Graph Together

13 min

Class uses Graph the Inequality.

👩‍🏫 Teacher Moves

  • Set the boundary and type.
  • Read the graph.
  • Explain the shading.

🎒 Student Actions

  • Set it.
  • Read it.
  • Explain it.
4

You Do — On Your Own

12 min

Students solve.

👩‍🏫 Teacher Moves

  • Solve inequalities.
  • Graph the solutions.
  • Flip the sign for negatives.

🎒 Student Actions

  • Solve them.
  • Graph them.
  • Flip when needed.
5

Close — Close

5 min

One inequality.

👩‍🏫 Teacher Moves

  • Give an inequality.
  • Solve and graph it.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve it.
  • Graph it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School Algebra).

CCSS
A-REI.3

Solve linear inequalities in one variable.

CCSS
A-REI.12

Graph the solutions to a linear inequality.

CCSS
A-CED.1

Create inequalities to model situations.

CCSS
A-REI.1

Explain each step in solving.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Open/closed circle cards.
  • Sentence frame: “x ___ ___ means ___.”
  • Use a number-line model.

Support & Access

IEP / 504
  • Start with one-step inequalities.
  • Use a number line.
  • Focus on the circle type.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Solve compound inequalities.
  • Solve two-step inequalities.
  • Write an inequality from a word problem.
Materials

What to gather

  • 📽️Projector / board
  • 📐Number lines
  • 💻Graph the Inequality
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

inequalitya comparison with >, <, ≥, or ≤solution setall values that make it trueopen circlea boundary NOT included (>, <)closed circlea boundary included (≥, ≤)boundarythe endpoint valueflip the signreverse < and > for a negativenumber linea line of ordered numbersshadeto mark the solution region
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Solve: x + 4 > 7.
x > 3.
QUESTION 2
When do you flip the inequality sign?
When you multiply or divide both sides by a negative number.
QUESTION 3
For x ≥ 5, do you use an open or a closed circle at 5?
A closed circle (≥ includes 5).

Going deeper? Flip it.

Have students solve inequalities like −2x < 8 and discover they must flip the sign when dividing by a negative. A printable inequalities sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Solving InequalitiesFlip
Card 1
Term
Tap to flip →
Meaning
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Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Solving InequalitiesQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Solving InequalitiesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: boundary, closed circle, flip the sign, inequality, number line, open circle, shade, solution set
  1. a boundary included (≥, ≤)
  2. the endpoint value
  3. reverse < and > for a negative
  4. to mark the solution region
  5. a boundary NOT included (>, <)
  6. a line of ordered numbers
  7. all values that make it true
  8. a comparison with >, <, ≥, or ≤

Part B · Show what you learned

  1. Solve: x + 4 > 7.
  2. When do you flip the inequality sign?
  3. For x ≥ 5, do you use an open or a closed circle at 5?
Answer key — Part A: 1) closed circle · 2) boundary · 3) flip the sign · 4) shade · 5) open circle · 6) number line · 7) solution set · 8) inequality
Part B: 1) x > 3. 2) When you multiply or divide both sides by a negative number. 3) A closed circle (≥ includes 5).