PEMDAS: Order of Operations
6-8
1
Solving Equations with Variables on Both Sides
Lesson Details
Grade Level
6-8
Duration (minutes)
1
Summary
An Algebra lesson on solving linear equations with variables on both sides, walked through step-by-step with the equation 3x + 2 = x + 10, ending with a substitution check.
Student Worksheet: Variables on Both Sides
Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!
Key Concepts:
• Get the Variable Alone: When x appears on both sides of an equation, first combine the x terms onto one side.
• Balance the Equation: Whatever you do to one side (subtract, add, divide), you must do to the other side too.
• Check Your Work: Substitute your answer back into the original equation to confirm both sides are equal.
Instructions: Solve each equation for x. Show your work by rewriting the equation after each step.
- Question 1: What is the first step in solving 3x + 2 = x + 10?
- Question 2: After subtracting x from both sides, what does the equation become?
- Question 3: After subtracting 2 from both sides, what does the equation become?
- Question 4: What is the final value of x?
- Question 5: Substitute x = 4 back into the original equation. Do both sides match?
- Question 6: Solve this new equation on your own: 5x + 3 = 2x + 18.
Click to reveal Teacher Answer Key
1. Subtract x from both sides.
2. 2x + 2 = 10
3. 2x = 8
4. x = 4
5. Yes — 3(4) + 2 = 14, and 4 + 10 = 14.
6. x = 5 (subtract 2x: 3x + 3 = 18; subtract 3: 3x = 15; divide by 3: x = 5)
Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.
🎯 Extension Activity: Have students write their own "variables on both sides" equation that solves to a whole number, trade with a partner, and solve each other's equation — then check the answer together using substitution.