AlgebraVery hardConstant that makes an equation an identity
Algebra practice question
The equation 2(4x − 1) − 5x = 3x + c, where c is a constant, is true for every value of x. What is the value of c?
Answer: -2 or −2
Simplify the left side: 8x − 2 − 5x = 3x − 2. For 3x − 2 = 3x + c to hold for every x, c must be −2.
Common wrong answers
- If you answered 2
- 2 has the wrong sign: 2(4x − 1) contributes −2, not +2.
- If you answered 8
- 8 is the coefficient 2 × 4 from the expansion, not the constant.
- If you answered -1
- −1 forgets to multiply the −1 inside the parentheses by 2.
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