Solving Equations with Variables on Both Sides


In earlier lessons, we solved equations like:

x + 3 = 7  

But now we’ll learn how to solve when x appears on both sides of the equation.


🔹 Example 1:

Solve: x + 2 = x + 5


Step 1: Subtract x from both sides:

x + 2 − x = x + 5 − x  

2 = 5


This is false → ❌ No solution


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🔹 Example 2:

Solve: 2x + 3 = x + 7


Step 1: Subtract x from both sides:

2x + 3 − x = x + 7 − x  

x + 3 = 7


Step 2: Subtract 3 from both sides:

x = 4


✅ Answer: x = 4


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🔹 Example 3:

Solve: 3x − 2 = 2x + 5


Step 1: Subtract 2x from both sides:

x − 2 = 5


Step 2: Add 2 to both sides:

x = 7


✅ Answer: x = 7


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✨ Tip:

Always move all x terms to one side and numbers to the other.


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✅ Practice Questions:


1. 2x + 1 = x + 6  

2. 3x − 4 = 2x + 3  

3. 5x + 2 = 2x + 11  

4. x + 7 = x + 2


📩 Drop your answers in the comments!

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