Answer
\[x=0\]
Work Step by Step
The equation is\[0.5\left( x+2 \right)=0.1+3\left( 0.1x+0.3 \right)\].
Use the order of operations,
\[\begin{align}
& 0.5\left( x+2 \right)=0.1+3\left( 0.1x+0.3 \right) \\
& 0.5x+1=0.1+0.3x+0.9 \\
& 0.5x+1=0.3x+1
\end{align}\]
Subtract \[1\] from both sides of the equal sign,
\[\begin{align}
& 0.5x+1-1=0.3x+1-1 \\
& 0.5x=0.3x
\end{align}\]
Subtract \[0.3x\] from both sides of the equal sign,
\[\begin{align}
& 0.5x-0.3x=0 \\
& 0.2x=0 \\
& x=\frac{0}{0.2} \\
& x=0
\end{align}\]
Therefore, \[x=0\]
