MathIsimple

Lesson 3-2: Solving Simple Equations

Master solving one-step equations using inverse operations with pizza party scenarios!

Learning Scenario: Pizza Party

Scenario: You're planning a pizza party for your friends. You know that each pizza costs $12, and you have $60 to spend. How many pizzas can you buy?

What We Need to Find:

  • • Number of pizzas you can buy
  • • Cost per pizza: $12
  • • Total money available: $60
  • • We need to solve: 12x = 60

Tools We'll Use:

  • • One-step equations
  • • Inverse operations
  • • Balancing equations
  • • Real-world verification

Understanding Equations

What is an Equation?

An equation is a mathematical statement that shows two expressions are equal. It has an equals sign (=) and usually contains a variable that we need to find.

12x = 60

This means: 12 times some number equals 60

Left Side: 12x

12 times the number of pizzas (x)

Right Side: 60

Total money available ($60)

Solving with Inverse Operations

What are Inverse Operations?

Inverse operations are operations that "undo" each other. They help us solve equations by isolating the variable.

Addition ↔ Subtraction

Multiplication ↔ Division

Example 1

If x + 5 = 12, then x = 12 - 5 = 7

Example 2

If 3x = 15, then x = 15 ÷ 3 = 5

Solving Our Pizza Problem

Let's solve 12x = 60 step by step:

12x = 60

Original equation

12x ÷ 12 = 60 ÷ 12

Divide both sides by 12 (inverse of multiplication)

x = 5

Solution: You can buy 5 pizzas!

Balancing Equations

The Balance Rule

Think of an equation like a balanced scale. Whatever you do to one side, you must do to the other side to keep it balanced.

12x

Left side

=
60

Right side

What We Did

Divided both sides by 12 to isolate x

Why It Works

Keeps the equation balanced and true

Practice Problems

Problem 1: Movie Tickets

Movie tickets cost $8 each. You have $40. How many tickets can you buy?

8x = 40

Write the equation

x = 40 ÷ 8 = 5

Solve using inverse operations

Answer: You can buy 5 movie tickets.

Problem 2: More Practice

Solve: x + 7 = 15

x = 15 - 7 = 8

Solve: 4x = 28

x = 28 ÷ 4 = 7

Checking Solutions

Always Check Your Answer

After solving an equation, always substitute your answer back into the original equation to make sure it's correct.

Original: 12x = 60

Our solution was x = 5

Check: 12(5) = 60

Substitute x = 5

60 = 60 ✓

Both sides are equal - our answer is correct!

Key Takeaways

Solving Equations

  • Use inverse operations to isolate the variable
  • Keep the equation balanced (do the same to both sides)
  • Always check your answer by substituting back
  • Practice with real-world problems

Remember

  • Addition and subtraction are inverse operations
  • Multiplication and division are inverse operations
  • Think of equations as balanced scales
  • Work step by step and show your thinking