Answer
$a=-\dfrac{61}{115}$
Work Step by Step
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ then
\begin{array}{l}\require{cancel}
0.1(a-0.2)=1.2+2.4a
\\\\
0.1(a)+0.1(-0.2)=1.2+2.4a
\\\\
0.1a-0.02=1.2+2.4a
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
0.1a-0.02=1.2+2.4a
\\\\
100(0.1a-0.02)=100(1.2+2.4a)
\\\\
10a-2=120+240a
\\\\
10a-240a=120+2
\\\\
-230a=122
\\\\
a=\dfrac{122}{-230}
\\\\
a=\dfrac{\cancel2(61)}{\cancel2(-115)}
\\\\
a=\dfrac{61}{-115}
\\\\
a=-\dfrac{61}{115}
.\end{array}
