MathIsimple
Lesson 5-2

Simple Equations

Master solving simple equations using balance scales and inverse operations. Learn equation solving through balance scale laboratory activities.

Learning Scenario: Balance Scale Laboratory

Scenario: You're in a balance scale laboratory! You have a balance scale with x + 3 on the left side and 7 on the right side. The scale is balanced, which means both sides are equal. You need to find the value of x that makes this true. What do you do?

This laboratory will teach you how to solve equations using the balance scale method - whatever you do to one side, you must do to the other to keep it balanced!

What are Equations?

An equation is a mathematical statement that shows two expressions are equal. It has an equals sign (=) between them.

Examples:

  • • x + 3 = 7
  • • 2y = 10
  • • n - 4 = 8
  • • a ÷ 2 = 5
Balance Scale Method

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

Key Rule:

Keep the equation balanced by doing the same operation to both sides

Step-by-Step Learning
1

Identify the Operation

Look at what operation is being done to the variable. Is it addition, subtraction, multiplication, or division?

Example: x + 3 = 7 → addition is being done to x

2

Use Inverse Operations

To solve for the variable, use the inverse (opposite) operation. Do the same to both sides to keep the equation balanced.

Example: x + 3 = 7 → subtract 3 from both sides → x = 4

3

Check Your Answer

Substitute your answer back into the original equation to make sure it works.

Example: x = 4, so 4 + 3 = 7 ✓ (correct!)

Interactive Activities

Activity 1: Balance Scale Practice

Solve these equations using the balance scale method:

  • • x + 2 = 8
  • • y - 3 = 5
  • • 2n = 12
  • • a ÷ 4 = 3
  • • b + 7 = 15

Activity 2: Equation Building

Write equations for these situations:

  • • A number plus 5 equals 12
  • • 3 times a number equals 18
  • • A number minus 4 equals 9
  • • A number divided by 2 equals 6
  • • 7 more than a number equals 20
Practice Problems

Problem Set 1: Addition Equations

1. x + 4 = 9

2. y + 6 = 14

3. n + 8 = 15

4. a + 3 = 11

Problem Set 2: Subtraction Equations

5. x - 2 = 7

6. y - 5 = 12

7. n - 3 = 9

8. a - 6 = 8

Problem Set 3: Multiplication & Division

9. 2x = 10

10. 3y = 18

11. x ÷ 4 = 3

12. y ÷ 2 = 7

Common Mistakes to Avoid

❌ Not doing the same operation to both sides

Wrong: x + 3 = 7 → x = 7 (only subtracted from left side)

Correct: x + 3 = 7 → x + 3 - 3 = 7 - 3 → x = 4

❌ Forgetting to check your answer

Wrong: Solving x + 3 = 7 and getting x = 4, but not checking

Correct: Always check: 4 + 3 = 7 ✓

Key Takeaways

Equations show that two expressions are equal

Use inverse operations to solve for the variable

Always do the same operation to both sides

Check your answer by substituting it back into the original equation