Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

If $\dfrac{\frac{x}{4}}{2}=\dfrac{4}{\frac{x}{2}}$ , then $x=$
$\text{(A)}\ \pm\frac{1}{2}$ $\text{(B)}\ \pm 1$ $\text{(C)}\ \pm 2$ $\text{(D)}\ \pm 4$ $\text{(E)}\ \pm 8$

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

Cross-multiplying leaves
$\begin{align*}\dfrac{x^2}{8} &= 8\\ x^2 &= 64\\ \sqrt{x^2} &= \sqrt{64}\\ x &= \pm 8\end{align*}$
So the answer is $\boxed{\text{(E)} \, \pm 8}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.