AlgebraVery hardConstant that makes an equation an identity
Algebra practice question
In the equation 5(x − 2) = 5x + k, k is a constant. If the equation is true for every value of x, what is the value of k?
Answer: -10 or −10
5(x − 2) = 5x − 10. For the two sides to match for all x, k must be −10.
Common wrong answers
- If you answered 0
- 0 would give 5x − 10 = 5x, which is never true.
- If you answered 10
- 10 has the wrong sign; 5 × (−2) = −10.
- If you answered -2
- −2 forgets to multiply by 5.
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