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Lesson 3-2: Solving Linear Equations

Scenario: Savings Goals - Learn to solve equations by planning your savings!

Duration: 60-75 minutesScenario: Savings Goals

Learning Objectives

  • Solve one-step equations using inverse operations
  • Solve multi-step equations systematically
  • Work with equations containing fraction coefficients
  • Apply equation solving to real-world savings problems

Savings Goal Scenario

The Problem

Sarah has $120 in her savings account. She wants to save $300 total. She plans to save $15 per week. How many weeks will it take to reach her goal?

Setting up the equation:
Current savings + (Weekly savings × Number of weeks) = Goal
120 + 15x = 300

Solving the Equation

Step 1: Subtract 120 from both sides

120 + 15x - 120 = 300 - 120
15x = 180

Step 2: Divide both sides by 15

15x ÷ 15 = 180 ÷ 15
x = 12

Answer: It will take 12 weeks to reach the savings goal.

One-Step Equations

Inverse Operations

Key Rule: To solve equations, use inverse operations to isolate the variable.

  • • Addition ↔ Subtraction
  • • Multiplication ↔ Division

Examples

Example 1: Addition

x + 7 = 15
x + 7 - 7 = 15 - 7
x = 8

Example 2: Multiplication

3x = 21
3x ÷ 3 = 21 ÷ 3
x = 7

Multi-Step Equations

Solving Strategy

Order of Operations (Reverse):

  1. 1. Remove parentheses (distribute if needed)
  2. 2. Combine like terms
  3. 3. Move variable terms to one side, constants to the other
  4. 4. Solve using inverse operations

Example with Parentheses

Solve: 2(x - 3) + 5 = 13

Step 1: Distribute

2(x - 3) + 5 = 13
2x - 6 + 5 = 13

Step 2: Combine like terms

2x - 1 = 13

Step 3: Add 1 to both sides

2x = 14

Step 4: Divide by 2

x = 7

Practice Problems

Problem 1: One-Step Equation

Solve: x - 8 = 15

Your solution:

Problem 2: Multi-Step Equation

Solve: 3x + 7 = 22

Your solution:

Problem 3: Real-World Application

A gym membership costs $25 per month plus a $50 sign-up fee. If you pay $175 total, how many months did you use the membership?

Your calculation: