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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.

  1. Sugar · Subtract 2x from both sides. What do you get?
    Student · 3x − 4 = 11.
  2. Sugar · Add 4 to both sides.
    Student · 3x = 15.
  3. Sugar · And x?
    Student · x = 5.

Answer: x = 5. Check: 21 = 21.

Try 3 practice questions

  1. 1. Solve 7x + 2 = 3x + 14.

    Show answer

    x = 3

  2. 2. Solve 2x − 5 = 5x + 7.

    Show answer

    x = −4

  3. 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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Save this as a miss — practice it before your test