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If 22 < < 23, which of the following could be the value of x [#permalink]
1
\(2^2 < \frac{x}{2^6-2^4} < 2^3\)

My main aim is to get rid of the denominator in the middle term and to that effect I will first try and simplify it

\(2^2 < \frac{x}{2^4(2^2-1)} < 2^3\)

\(2^2 < \frac{x}{2^4(4-1)} < 2^3\)

\(2^2 < \frac{x}{16 \times 3} < 2^3\)

\(4 < \frac{x}{48} < 8\)

Now, I get rid of the denominator \(48\) in the middle term by multiplying throughout by \(48\)

\(192 < x < 384\)

Thus the correct answers are E and F.
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