Answer
$ m\leq 15$
The graph is shown below.

Work Step by Step
The given inequality is
$\Rightarrow 1+\frac{m}{3} \leq 6$
Subtract $1$ from each side.
$\Rightarrow 1+\frac{m}{3} -1\leq 6-1$
Simplify.
$\Rightarrow \frac{m}{3} \leq 5$
Multiply each side by $3$.
$\Rightarrow 3\cdot \frac{m}{3}\leq 3\cdot 5$
Simplify.
$\Rightarrow m\leq 15$
Hence, the solution is $ m\leq 15$.
Use a close circle because $15$ is a solution.
Shade the number line on the left side.