AlgebraVery hardCondition for an equation to have no solution
Algebra practice question
The equation 5x + 3 = 5x + c, where c is a constant, has no solution. Which of the following must be true?
- A. c ≠ 3Correct
- B. c = 3
- C. c = 0
- D. c = 5
Answer: A. c ≠ 3
The x-terms cancel, leaving 3 = c. If c is anything other than 3 the statement is false for every x; if c = 3 every x works.
Why the other answers are wrong
- B. c = 3
- c = 3 gives infinitely many solutions.
- C. c = 0
- c = 0 works, but so does every value except 3.
- D. c = 5
- c = 5 works, but so does every value except 3.
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