⚖️ Solving Linear Equations

Find the unknown and keep everything balanced!

🎯 What You'll Learn

Understand equations as balanced mathematical statements
Use inverse operations to solve for unknown variables
Solve one-step and two-step linear equations
Check solutions by substitution

💡 Why This Chapter Matters

Solving equations is like being a mathematical detective! Whether you're calculating how many hours you need to work to afford something, figuring out mixing ratios for recipes, or determining speeds and distances, equations help you find unknown values in real-world situations.

⚖️ The Balance Model

Think of equations like a balance scale. Both sides must always be equal!

x + 3

x + 3 = 12
To keep the balance, whatever we do to one side, we must do to the other!

Click "Subtract 3" to see how we solve for x!

x + 8 = 15

x =

Enter your answer and click "Check Answer"

🌟 Real-World Equation

Problem: Sarah has some stickers. After giving away 15 stickers, she has 23 left. How many stickers did she start with?

Step 1: Set up the equation

Let x = number of stickers Sarah started with

x - 15 = 23

Step 2: Solve by adding 15 to both sides

x - 15 + 15 = 23 + 15

x = 38

Step 3: Check the answer

38 - 15 = 23 ✓

Answer: Sarah started with 38 stickers.

🔧 Step-by-Step Equation Solver

Choose an equation to solve, or click solve to see the steps:

x + 5 = 13

📚 Types of Linear Equations

Addition Equations

x + 7 = 15

Subtract the same number from both sides to solve

Subtraction Equations

x - 4 = 9

Add the same number to both sides to solve

Multiplication Equations

3x = 21

Divide both sides by the coefficient to solve

Division Equations

x ÷ 5 = 6

Multiply both sides by the divisor to solve

💪 Practice Exercises

1. Solve for x: x + 9 = 17

2. Solve for x: 4x = 28

3. Solve for x: 2x + 3 = 15

4. Solve for x: x - 4 = 11

5. Solve for x: 3x = 18

⚠️ Common Mistakes

Forgetting to do the same operation to both sides
Not checking your answer by substitution
Mixing up operations (adding instead of subtracting)

✨ Quick Summary

Think of equations as balanced scales—whatever you do to one side, do to the other. Use inverse operations to isolate the variable and always check your answer!