Question

\[\frac{x - 1}{3} + 4 < \frac{x - 5}{5} - 2\]

Answer 1

\[\frac{x - 1}{3} + 4 < \frac{x - 5}{5} - 2\]
\[ \Rightarrow \frac{x - 1}{3} - \frac{x - 5}{5} < - 2 - 4 \left[ \text{ Transposing 4 to the RHS and \frac{x - 5}{5} to the LHS } \right]\]
\[ \Rightarrow \frac{5\left( x - 1 \right) - 3\left( x - 5 \right)}{15} < - 6\]
\[ \Rightarrow \frac{5x - 5 - 3x + 15}{15} < - 6\]
\[ \Rightarrow \frac{2x + 10}{15} < - 6\]
\[ \Rightarrow 2x + 10 < - 90\]
\[ \Rightarrow 2x < - 90 - 10 \left[ \text{ Transposing 10 to the RHS } \right]\]
\[ \Rightarrow 2x < - 100 \]
\[ \Rightarrow x < - \frac{100}{2} \left[ \text{ Dividing both the sides by 2 } \right]\]
\[ \Rightarrow x < - 50\]
\[\text{ Hence, the solution of the given inequation is } \left( - \infty , - 50 \right) . \]