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.
- Subtract 2x from both sides: 3x − 7 = 11.
- Add 7 to both sides: 3x = 18.
- 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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