AlgebraVery hardCounting solutions of a simplifying equation
Algebra practice question
How many solutions does the equation 3(x − 2) − 2(x − 3) = x have?
- A. Infinitely manyCorrect
- B. Exactly one
- C. None
- D. Exactly two
Answer: A. Infinitely many
Expand: 3x − 6 − 2x + 6 = x, which simplifies to x = x. That is true for every value of x, so every number is a solution.
Why the other answers are wrong
- B. Exactly one
- After simplifying, no single value of x is singled out; both sides are identical.
- C. None
- x = x is never false, so there are solutions — all of them.
- D. Exactly two
- A linear equation can't have exactly two solutions.
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