AlgebraVery hardConstant that makes an identity
Algebra practice question
The equation 2(3x − k) = 6x − 10, where k is a constant, is true for every value of x. What is the value of k?
Answer: 5
Expand: 6x − 2k = 6x − 10. For this to hold for every x, the constants must match: 2k = 10, so k = 5.
Common wrong answers
- If you answered 3
- 3 is the coefficient of x inside the parentheses, not k.
- If you answered 10
- 10 is 2k; the 2 outside the parentheses multiplies k as well.
- If you answered -5
- −5 has the wrong sign: −2k = −10 gives k = 5.
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