Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $2 x^{2}=9 x-4$ and $x
eq 4 $, what is the value of$ 2 x$?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $2 x^{2}=9 x-4$ , then $2 x^{2}-9 x+4=0$ . Factoring, we obtain $(2 x-1)(x-4)=0$ . Thus, $2 x=1$ or $x=4$ . Since $x
eq 4 $, then$ 2 x=1$.

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