Solving Multi-Step Equations

Lesson 3 of 10Grades 8–9

Most real equations take more than one step to solve. The strategy: simplify each side first (distribute, combine like terms), then move variables to one side and constants to the other using inverse operations.

Key Concepts

Two-Step Equations

2x + 3 = 11. Step 1: subtract 3 from both sides → 2x = 8. Step 2: divide by 2 → x = 4. Always undo addition/subtraction first, then multiplication/division. Think of peeling an onion — work from outside in.

Variables on Both Sides

3x + 5 = x + 13. Move all x terms to one side: subtract x from both sides → 2x + 5 = 13. Subtract 5 → 2x = 8. Divide by 2 → x = 4. Check: 3(4)+5=17, 4+13=17 ✓.

Special Cases

No solution: x + 3 = x + 7 → 3 = 7 (false for all x). Infinite solutions: 2x + 4 = 2(x + 2) → 4 = 4 (true for all x). When the variable cancels, check if the remaining statement is true or false.

🆕 Multi-Step Equation Solver

Solve equations step-by-step. Try: 2x+3=11, 3x+5=x+13, 5(x-2)=15

✅ Check Your Understanding

1. Solve 2x + 5 = 13. What is x?

2. To solve 5x + 3 = 2x + 12, first move x terms. You get...

3. If solving gives '5 = 8', the equation has...