Lesson 83: One-Step Equations

Page Menu

• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson introduces one-step equations and teaches students how to isolate variables using inverse operations. Students will learn how equations represent balanced mathematical statements and how to maintain equality while solving for unknown values.

Learning Objectives

• Solve one-step equations using addition, subtraction, multiplication, and division.
• Apply inverse operations to isolate variables.
• Verify solutions by substitution.

Topics Covered

• Understanding equations and variables
• Inverse operations
• Balancing equations

Key Terms

• Equation: A mathematical statement showing two expressions are equal.
• Variable: A symbol representing an unknown value.
• Inverse Operation: An operation that reverses another operation.

Lesson Examples

Example 1: Solving Using Addition or Subtraction

1. Solve: x + 5 = 12
2. Subtract 5 from both sides: x = 7
3. Check: 7 + 5 = 12 ✓

Example 2: Solving Using Multiplication or Division

1. Solve: 4x = 20
2. Divide both sides by 4: x = 5
3. Check: 4 × 5 = 20 ✓

Practice Problems

1. x + 9 = 15
2. x - 6 = 10
3. 3x = 21
4. x ÷ 5 = 4

Tips & Common Mistakes

• Always perform the same operation on both sides of the equation.
• Use inverse operations carefully to isolate the variable.
• Always check your answer by substituting it back into the original equation.

Summary

One-step equations require only one operation to solve. By using inverse operations and maintaining balance on both sides of the equation, you can easily isolate the variable and determine its value.

Challenge Problems

1. x + 13 = 28
2. 7x = 56
3. x ÷ 8 = 9