Answer
$X=2$
Work Step by Step
The elements of $\;\mathbb{Z}_{5}\;$ are 0,1,2,3,4
So, if there is a solution for this equation, then x is one of these numbers.
$If \;\;x=0\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;2.(0)+3=2 \; {\color{Red}\rightarrow } \;\; 0+3= 2\;\;{\color{Red} \Rightarrow }\;\;3\neq 2\\
so \;\;0 \;is \;not \;solution\\\\
If \;x=1\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;2.(1)+3=2 \; {\color{Red}\rightarrow } \;\; 2+3= 2\;\;{\color{Red} \Rightarrow }\;\;0\neq 2\\
so\; 1\; is\; not\;solution.\\\\
If\;x=2\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;2.(2)+3=2 \; {\color{Red}\rightarrow } \;\; 4+3= 2\;\;{\color{Red} \Rightarrow }\;\;2= 2\\
so\; 2\; is\;SOLUTION\\\\
If \;x=3\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;2.(3)+3=2 \; {\color{Red}\rightarrow } \;\; 1+3= 2\;\;{\color{Red} \Rightarrow }\;\;4\neq 2\\
so\; 3\; is\; not\; solution\\\\
If\; x=4\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;2.(4)+3=2 \; {\color{Red}\rightarrow } \;\; 3+3= 2\;\;{\color{Red} \Rightarrow }\;\;1\neq 2\\
so\; 4 \;is\; not\; solution\\\\$
$X=2$
