Lesson 3-2: Multi-step Equations

Scenario: Savings Planning - Solve equations to plan your savings goals!

Duration: 55-70 minutesScenario: Savings Planning

Learning Objectives

Solve multi-step equations using inverse operations
Work with equations containing fractions and decimals
Apply equation properties to maintain equality
Verify solutions by substitution

Savings Goal Problem

Monthly Savings Plan

Xiao Ming has $x in his savings account. He plans to save $15.50 per month for 3 months. After 3 months, he wants to have $100 total. How much did he start with?

Problem: x + 3 × 15.50 = 100

Step-by-Step Solution

Step 1: Write the equation

x + 3 × 15.50 = 100

Step 2: Simplify the multiplication

x + 46.50 = 100

Step 3: Solve for x

x = 100 - 46.50 = 53.50

Step 4: Verify the solution

53.50 + 46.50 = 100 ✓

Answer: Xiao Ming started with $53.50.

Fraction Equations

Example 1

Solve: (x/2) + 3 = 7

Solution:
(x/2) + 3 = 7
x/2 = 7 - 3 = 4
x = 4 × 2 = 8

Example 2

Solve: (2/3)x - 5 = 1

Solution:
(2/3)x - 5 = 1
(2/3)x = 1 + 5 = 6
x = 6 × (3/2) = 9

Practice Problems

Problem 1

Solve: 2x + 7 = 15

Your solution:

Problem 2

A student has $x. After buying 4 notebooks at $2.50 each, she has $8 left. How much did she start with?

Your solution:

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