Answer
$a\ge\dfrac{115}{57}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-1.4a+2.34a+6.1\ge-0.2a+8.4
,$ use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-1.4a+2.34a+6.1\ge-0.2a+8.4
\\\\
-1.4a+2.34a+0.2a\ge8.4-6.1
\\\\
1.14a\ge2.3
\\\\
100(1.14a)\ge100(2.3)
\\\\
114a\ge230
\\\\
a\ge\dfrac{230}{114}
\\\\
a\ge\dfrac{\cancel{2}(115)}{\cancel{2}(57)}
\\\\
a\ge\dfrac{115}{57}
.\end{array}
