Question
$\frac{x}{2}+5 \leq \frac{x}{3}+6$ where $x$ is a positive odd integer.
✓
Answer
$
\begin{aligned}
& \frac{x}{2}+5 \leq \frac{x}{3}+6 \\
& \Rightarrow \frac{x}{2}-\frac{x}{3} \leq 6-5 \\
& \Rightarrow \frac{3 x-2 x}{6} \leq 1 \\
& \Rightarrow \frac{x}{6} \leq 1 \\
& \Rightarrow x \leq 6
\end{aligned}
$
$\because x$ is a positive odd integer
$
\therefore x=\{1,3,5\} .
$
\begin{aligned}
& \frac{x}{2}+5 \leq \frac{x}{3}+6 \\
& \Rightarrow \frac{x}{2}-\frac{x}{3} \leq 6-5 \\
& \Rightarrow \frac{3 x-2 x}{6} \leq 1 \\
& \Rightarrow \frac{x}{6} \leq 1 \\
& \Rightarrow x \leq 6
\end{aligned}
$
$\because x$ is a positive odd integer
$
\therefore x=\{1,3,5\} .
$
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