Solving with variables on both sides
Move all x terms to one side before solving.
The common mistake
Adding x terms across the equals sign instead of subtracting — 5x = 2x + 9 becoming 7x = 9.
Instead: Do the same operation to both sides: subtract the smaller x term from both sides, then solve the two-step equation that's left.
Worked example with Guide me
Solve 5x − 4 = 2x + 11.
- Sugar · Subtract 2x from both sides. What do you get?Student · 3x − 4 = 11.
- Sugar · Add 4 to both sides.Student · 3x = 15.
- Sugar · And x?Student · x = 5.
Answer: x = 5. Check: 21 = 21.
Try 3 practice questions
1. Solve 7x + 2 = 3x + 14.
Show answer
x = 3
2. Solve 2x − 5 = 5x + 7.
Show answer
x = −4
3. Solve 9 − x = x + 1.
Show answer
x = 4
Quick answers
- What is the most common mistake with solving with variables on both sides?
- Adding x terms across the equals sign instead of subtracting — 5x = 2x + 9 becoming 7x = 9.
- How do I get solving with variables on both sides right?
- Do the same operation to both sides: subtract the smaller x term from both sides, then solve the two-step equation that's left.
- Can you show a worked example?
- Solve 5x − 4 = 2x + 11. x = 5. Check: 21 = 21.
Related concepts
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