Advanced MathHardEquation with a common factor on both sides
Advanced Math practice question
What is the sum of all solutions of the equation (x − 2)(x + 5) = (x − 2)(2x − 1)?
Answer: 8
Bring everything to one side: (x − 2)[(x + 5) − (2x − 1)] = (x − 2)(6 − x) = 0. The solutions are x = 2 and x = 6, whose sum is 8.
Common wrong answers
- If you answered 2
- 2 is one solution.
- If you answered 6
- 6 is the only solution if you divide both sides by (x − 2), which loses x = 2.
- If you answered 12
- 12 is the product of the solutions.
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