Question

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

• A. $\frac{9x}{5}+\frac{q}{2}$
• B. $\frac{9x}{4}-\frac{q}{2}$
• C. $\frac{9x}{5}-\frac{q}{2}$
• D. $\frac{11x}{5}+2q$

Answer 1

The correct option is D $\frac{11x}{5}+2q$

$\frac{1}{4}x-5(q-x)-\frac{3}{2}(\frac{1}{3}(q-\frac{x}{3})-\frac{2}{9}[x-\frac{3}{4}(q-\frac{4x}{5})])$

$=(\frac{1}{4}x-5q+5x)-\frac{3}{2}(\frac{9}{3}-\frac{x}{9})-\frac{2}{9}(x-\frac{3q}{4}+\frac{3x}{5})$

$=(\frac{x}{4}-5q+5x)-\frac{9}{2}+\frac{x}{6}-\frac{2x}{9}+\frac{9}{6}-\frac{2}{15}x$

$=(\frac{x}{4}+5x+\frac{x}{6}-\frac{2x}{9}-\frac{2}{15}x)+(-5q-\frac{q}{2}+\frac{q}{6})$

$=\frac{11x}{5}+2q$