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2002 AMC 10B Problems/Problem 13

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Problem

Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for all values of y.

\textbf{(A) } \frac23 \qquad \textbf{(B) } \frac32 \text{ or } -\frac14 \qquad \textbf{(C) } -\frac23 \text{ or } -\frac14 \q...

Solution

We have 8xy - 12y + 2x - 3 = 4y(2x - 3) + (2x - 3) = (4y + 1)(2x - 3).

As (4y + 1)(2x - 3) = 0 must be true for all y, we must have 2x - 3 = 0, hence \boxed{x = \frac 32}.

See Also

2002 AMC 10B (ProblemsResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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