Solving One-Step Inequalities

Lesson Overview

Grade Level: 7th grade
Subject: Mathematics
Duration: 40 minutes
Topic: Solving and Graphing One-Step Inequalities
Curriculum Area: CCSS.MATH.CONTENT.7.EE.B.4.B – Solve word problems leading to inequalities of the form px + q > r or px + q < r and graph the solution set.

---

Objectives

By the end of this lesson, students will be able to:

1. Solve one-step inequalities (using addition, subtraction, multiplication, or division).
2. Graph the solutions of inequalities on a number line.
3. Apply real-world scenarios to understand the practical applications of inequalities.

---

Materials Needed

• Whiteboard and markers
• Student notebooks
• Rulers for each student
• Pre-drawn number lines (on both the board and handouts)
• Student handouts with practice problems
• Sticky notes (one per student)
• Colored markers or pencils for graphing

---

Lesson Structure

1. Introduction (5 minutes)

Hook/Engagement Activity (2 minutes):
Begin by asking a question to spark curiosity:
"Imagine you're saving up for a new video game, and you need more than $50 to buy it. You’ve saved $30 already. How much more do you need?"

Write the inequality on the board:
30 + x > 50

• Explain that today, students will learn how math can help solve problems like these by using one-step inequalities.

Objective Overview (3 minutes):
Go over today’s objectives with the class:

• "We’re going to solve inequalities just like we solve equations – but there’s one major difference. Let’s find out what that is!"
• "We’ll also graph these solutions so you can see what all possible answers look like."

---

2. Instruction (13 minutes)

Step 1: Defining Inequalities (3 minutes)

• Write four inequality symbols on the board and explain their meanings:
  > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to).
• Emphasize that inequalities show a range of possible solutions rather than one specific answer.

Step 2: Solving One-Step Inequalities (7 minutes)

• Highlight the golden rule: Solving one-step inequalities is almost identical to equations, except:
  • When multiplying or dividing by a negative number, reverse the inequality sign.

Provide Examples (Do these together on the board):

1. Addition Inequality:

   • Solve: x - 5 ≤ 12
     Add 5 to both sides:
     x ≤ 17
   • Graph on a number line.

2. Multiplication or Division with a Negative:

   • Solve: -2x > 10
     Divide both sides by -2 (and reverse the sign):
     x < -5
   • Graph on a number line.

Invite student participation: Call on students to demonstrate how to solve an inequality step-by-step for each example.

Step 3: Graphing Inequalities (3 minutes)

• Draw a large number line on the whiteboard for x ≤ 17:
  • Review open vs. closed circles:
    • Use a closed circle for ≤ or ≥.
    • Use an open circle for < or >.
  • Shade the direction of the possible solutions.

Have students practice identifying whether to use open or closed circles. Call on individual students to explain their reasoning.

---

3. Practice and Application (10 minutes)

Scenario-Based Problem (3 minutes)

Provide a real-world problem for students to solve collaboratively. Write the problem on the board:
"Sam’s basketball team is selling raffle tickets to earn at least $200. Each ticket costs $5. How many tickets must Sam sell?"

• Guide students to write the inequality:
  5x ≥ 200
  Solve:
  x ≥ 40
  Graph on a number line.
• Discuss: Why is it important to use a closed circle here? What does shading to the right mean?

Paired Work (7 minutes)

1. Hand out practice sheets with 4 problems to solve and graph.
   Examples:
   • x + 8 > 15
   • x / 3 ≤ 6
   • -4x < 20
   • 7x ≥ 42
2. Each pair solves and graphs together. Encourage peer discussion by having one partner explain their reasoning while the other follows along.

---

4. Reflection and Wrap-Up (7 minutes)

Class Discussion (3 minutes)

• Ask:
  "Why is it important to flip the inequality sign when dividing by a negative number?"
  "How are inequalities useful in everyday life?"

Encourage students to come up with their own real-world examples of inequalities.

Exit Ticket (4 minutes)

• Provide sticky notes and ask students to complete:
  Solve and graph:
  3x + 2 < 11
  Collect sticky notes as they leave for review and quick assessment of the day’s learning.

---

Homework (Optional)

1. Solve and graph 5 inequalities on a worksheet.
2. Write one real-world situation that could be represented by an inequality. Solve it!

---

Extensions/Enrichment

• Challenge advanced learners: Introduce compound inequalities (e.g., -3 < x + 2 ≤ 5) for those who need more rigor.
• For students needing support: Provide a visual "cheat sheet" of steps to solve inequalities, with example graphs for reference.

---

Assessment and Evaluation

• Informal checks for understanding during class participation and paired work.
• Review of sticky note exit tickets to identify individual or class-wide misconceptions.
• Homework review for reinforcement in the next lesson.

---

Teacher Notes

1. Keep the energy upbeat during groupwork by circulating around the room and providing encouragement.
2. If students struggle with graphing, pause and review number line basics before progressing.