#### Answer

$x=\dfrac{404}{185}$

#### Work Step by Step

Using the properties of equality, the value of the variable that satisfies the given expression, $
1.8x+0.16=4.2-0.05x
,$ is
\begin{array}{l}\require{cancel}
1.8x+0.05x=4.2-0.16
\\\\
1.85x=4.04
\\\\
x=\dfrac{4.04}{1.85}
\\\\
x=\dfrac{4.04}{1.85}\cdot\dfrac{100}{100}
\\\\
x=\dfrac{404}{185}
.\end{array}