#### Answer

$x=-4$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2.1x+45.2=3.2-8.4x
,$ remove first the decimal numbers by multiplying both sides by a power of $10.$ Then use the properties of equality to isolate the variable. Do checking of the solution.
$\bf{\text{Solution Details:}}$
Since the largest number of decimal places a term has is $1,$ multiply both sides by $10.$ This results to
\begin{array}{l}\require{cancel}
2.1x+45.2=3.2-8.4x
\\\\
10(2.1x+45.2)=10(3.2-8.4x)
\\\\
21x+452=32-84x
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
21x+452=32-84x
\\\\
21x+84x=32-452
\\\\
105x=-420
\\\\
x=\dfrac{420}{105}
\\\\
x=-4
.\end{array}
Checking: If $x=-4,$ then
\begin{array}{l}\require{cancel}
2.1(-4)+45.2=3.2-8.4(-4)
\\\\
-8.4+45.2=3.2+33.6
\\\\
36.8=36.8
\text{ (TRUE) }
.\end{array}
Hence, the solution is $
x=-4
.$