Solve the system of inequalities:
$3x - 7 < 5 + x$ ..... $(1)$
$11 - 5x \leqslant 1$ ..... $(2)$
and represent the solutions on the number line.

(N/A) From inequality $(1)$,we have:
$3x - 7 < 5 + x$
$2x < 12$
$x < 6$ ..... $(3)$
From inequality $(2)$,we have:
$11 - 5x \leqslant 1$
$-5x \leqslant 1 - 11$
$-5x \leqslant -10$
Dividing by $-5$ reverses the inequality sign:
$x \geqslant 2$ ..... $(4)$
Combining $(3)$ and $(4)$,the solution is the set of all real numbers $x$ such that $2 \leqslant x < 6$.