AlgebraHardIdentifying an identity
Algebra practice question
Which of the following equations is true for EVERY value of x?
- A. 3(x + 2) − 6 = 3xCorrect
- B. 3(x + 2) = 3x + 2
- C. 2x + 5 = 2x − 5
- D. 4x = 4
Answer: A. 3(x + 2) − 6 = 3x
3(x + 2) − 6 = 3x + 6 − 6 = 3x, so the two sides are identical for every x.
Why the other answers are wrong
- B. 3(x + 2) = 3x + 2
- 3(x + 2) = 3x + 6, not 3x + 2. The equation is never true.
- C. 2x + 5 = 2x − 5
- 2x + 5 = 2x − 5 reduces to 5 = −5, which is never true.
- D. 4x = 4
- 4x = 4 is true only when x = 1.
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