Question

Solve: $\frac{4x+17}{18}-\frac{13x-2}{32}+\frac{x}{3}=\frac{7x}{12}-\frac{x+16}{36}$

• A. $\frac{418}{117}$
• B. $6$
• C. $1$
• D. $-\frac{8}{3}$

Answer 1

The correct option is A $\frac{418}{117}$

Given, $\frac{4x+17}{18}-\frac{13x-2}{32}+\frac{x}{3}=\frac{7x}{12}-\frac{x+16}{36}$
$\Rightarrow \frac{4x+17}{18}+\frac{x}{3}-\frac{7x}{12}+\frac{x+16}{36}=\frac{13x-2}{32}$
$\Rightarrow \frac{8x+34+12x-21x+x+16}{36}=\frac{13x-2}{32}$
$\Rightarrow \frac{50}{36}=\frac{13x-2}{32}$
$\Rightarrow \frac{50}{9}=\frac{13x-2}{8}$

On cross multiplying, we get
$400=117x-18$
$\Rightarrow 117x=418$
$\Rightarrow x=\frac{418}{117}$