AlgebraVery hardValue of a constant that removes all solutions
Algebra practice question
In the equation 2(3x + a) = 6x + 9, a is a constant. For which value of a does the equation have NO solution?
- A. Any value of a other than 4.5Correct
- B. a = 4.5 only
- C. a = 9 only
- D. No value of a
Answer: A. Any value of a other than 4.5
Expand: 6x + 2a = 6x + 9, so the x-terms cancel and the equation reduces to 2a = 9. If a = 4.5 this is always true (infinitely many solutions); for any other a it is false (no solution).
Why the other answers are wrong
- B. a = 4.5 only
- a = 4.5 gives infinitely many solutions, not none.
- C. a = 9 only
- a = 9 does give no solution, but so does every other value except 4.5.
- D. No value of a
- Every value except 4.5 gives no solution.
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