Answer
$f(x)=\begin{cases}
-2x+8,\text{ for } x\lt \frac{5}{2}\\
2x-2\text{ for } x\geq \frac{5}{2}
\end{cases}$
Work Step by Step
We are given the function:
$f(x)=3+|2x-5|$
Rewrite the function in piecewise form, using the fact that $|y|=-y$ for $y\lt 0$ and $|y|=y$ for $y\geq 0$:
$f(x)=\begin{cases}
3-(2x-5),\text{ for } 2x-5\lt 0\\
3+(2x-5)\text{ for } 2x-5\geq 0
\end{cases}$
$f(x)=\begin{cases}
3-2x+5,\text{ for } 2x\lt 5\\
3+2x-5\text{ for } 2x\geq 5
\end{cases}$
$f(x)=\begin{cases}
-2x+8,\text{ for } x\lt \frac{5}{2}\\
2x-2\text{ for } x\geq \frac{5}{2}
\end{cases}$
