AlgebraVery hardConstant that rescues an equation from having no solution
Algebra practice question
The equation 5x − 2(x + p) = 3x + 6, where p is a constant, has no solution unless p takes one particular value. What is that value of p?
Answer: -3
Simplifying: 3x − 2p = 3x + 6. The x-terms cancel, so the equation holds only if −2p = 6, that is, p = −3 (and then every x works).
Common wrong answers
- If you answered 0
- 0 makes the equation 3x = 3x + 6, which has no solution.
- If you answered 3
- 3 has the sign wrong: −2p = 6 gives p = −3.
- If you answered -6
- −6 forgets to divide by −2.
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