Explanation

(a)
Given equation is $|x - 4| + |x - 9| = 5$
$\Rightarrow \left\{ \begin{array}{r}
4 - x + 9 - x = 5,\ x \leq 4 \\
x - 4 + 9 - x = 5,\ 4 < x \leq 9 \\
x - 4 + x - 9 = 5,\ x > 9
\end{array} \right.\$
$\Rightarrow \left\{ \begin{array}{r}
x = 4,x \leq 4 \\
no\ solution,\ 4 < x \leq 9 \\
x = 9,x > 9
\end{array} \right.\$
So, $x = 4,\ 9$