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Question

The value of $$\dfrac{1}{4}{x - 5(q - x)}$$
$$-\dfrac{3}{2} (\dfrac{1}{3} (q - \dfrac{x}{3}) - \dfrac{2}{9}[x - \dfrac{3}{4}(q - \dfrac{4x}{5})])$$ is _______.


A
9x5+q2
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B
9x4q2
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C
9x5q2
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D
11x5+2q
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Solution

The correct option is D $$\dfrac{11x}{5} + 2q$$
$$\cfrac {1}{4}x-5(q-x)-\cfrac {3}{2}\left(\cfrac {1}{3}\left(q-\cfrac {x}{3}\right)-\cfrac {2}{9}\left [x-\cfrac {3}{4}\left(q-\cfrac {4x}{5}\right)\right]\right)$$
$$=\left(\cfrac {1}{4}x-5q+5x\right)-\cfrac{3}{2}\left (\cfrac {9}{3}-\cfrac {x}{9}\right)-\cfrac {2}{9}\left(x-\cfrac {3q}{4}+\cfrac {3x}{5}\right)$$
$$=\left (\cfrac {x}{4}-5q+5x\right)-\cfrac {9}{2}+\cfrac {x}{6}-\cfrac {2x}{9}+\cfrac{9}{6}-\cfrac {2}{15}x$$
$$=\left(\cfrac {x}{4}+5x+\cfrac {x}{6}-\cfrac {2x}{9}-\cfrac {2}{15}x\right)+\left(-5q-\cfrac {q}{2}+\cfrac {q}{6}\right)$$
$$=\cfrac {11x}{5}+2q$$

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