The absolute value is defined as
[tex] |x| = \begin{cases}x \text{ if } x\geq 0\\-x \text{ if } x < 0\end{cases} [/tex]
In your case, the expression inside the absolute value is [tex] x-3 [/tex], which changes sign at [tex] x=3 [/tex]. So, you have
[tex] 2|x-3|+5 = \begin{cases}2(x-3)+5 \text{ if } x\geq 3\\2(3-x)+5 \text{ if } x < 3\end{cases} [/tex]
