Question
Solve for $x, \frac{3 x-5}{17}+\left[\frac{11-x}{76}-\frac{3}{4}\right]=\frac{4+x}{2}-13$.
✓
Answer
We have, $\frac{3 x-5}{17}+\left[\frac{11-x}{76}-\frac{3}{4}\right]=\frac{4+x}{2}-13$
$\Rightarrow \quad \frac{3 x}{17}-\frac{5}{17}+\frac{11}{76}-\frac{x}{76}-\frac{3}{4}=2+\frac{x}{2}-13$
$\Rightarrow \quad \frac{3 x}{17}-\frac{x}{76}-\frac{x}{2}=-11+\frac{5}{17}-\frac{11}{76}+\frac{3}{4}$
$\Rightarrow \frac{456 x-34 x-1292 x}{2584}=\frac{-56848+1520-748+3876}{5168}$
$\Rightarrow \quad \frac{456 x-1326 x}{2584}=-\frac{52200}{5168}$
$\Rightarrow \quad \frac{-870 x}{2584}=\frac{-52200}{5168}$
$\Rightarrow \quad x=\frac{-52200}{5168} \times\left(\frac{-2584}{870}\right)$
$=\frac{60}{2}=30$
$\Rightarrow \quad \frac{3 x}{17}-\frac{5}{17}+\frac{11}{76}-\frac{x}{76}-\frac{3}{4}=2+\frac{x}{2}-13$
$\Rightarrow \quad \frac{3 x}{17}-\frac{x}{76}-\frac{x}{2}=-11+\frac{5}{17}-\frac{11}{76}+\frac{3}{4}$
$\Rightarrow \frac{456 x-34 x-1292 x}{2584}=\frac{-56848+1520-748+3876}{5168}$
$\Rightarrow \quad \frac{456 x-1326 x}{2584}=-\frac{52200}{5168}$
$\Rightarrow \quad \frac{-870 x}{2584}=\frac{-52200}{5168}$
$\Rightarrow \quad x=\frac{-52200}{5168} \times\left(\frac{-2584}{870}\right)$
$=\frac{60}{2}=30$
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