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How to Solve a Linear Equation by Transposing Terms

Quick answer: Transposing a term is shorthand for doing the same operation on both sides. Addition is undone by subtraction; multiplication by a nonzero number is undone by division.

Worked example

Solve 5x − 7 = 2x + 11.

  1. Subtract 2x from both sides: 3x − 7 = 11.
  2. Add 7 to both sides: 3x = 18.
  3. Divide both sides by 3: x = 6.

Check the result

Left side: 30 − 7 = 23. Right side: 12 + 11 = 23, so the solution satisfies the original equation.

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Common mistake to avoid

Do not change the sign of every symbol when moving just one term. A bracket such as −(x + 2) becomes −x − 2.

Try it yourself

1. Solve 4x + 3 = 19. 2. Solve 7 − 2x = 15.

Answers and reasoning

1. 4x = 16, hence x = 4. 2. −2x = 8, hence x = −4.

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