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Obtain the values of x for which the binomial expansions for the ${(3 - 4 x)}^{- 7}$

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$\frac{- 3}{4} < x < \frac{3}{4}$

$\frac{- 1}{4} < x < \frac{3}{4}$

$\frac{- 3}{4} < x < \frac{5}{4}$

$\frac{- 3}{2} < x < \frac{3}{5}$

answer is A.

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Detailed Solution

$\begin{array}{l} {(3 - 4 x)}^{- 7} \\ 3^{- 7} {(1 - \frac{4 x}{3})}^{- 7} \\ | \frac{- 4 x}{3} | < 1 \\ | x | < \frac{3}{4} \\ \frac{- 3}{4} < x < \frac{3}{4} \end{array}$

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