Answer
$k\le\dfrac{4416}{17}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
1.85+1.34(2.4k-5.7)\ge3.25k-14.62
,$ use the Distributive Property and the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property, which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
1.85+1.34(2.4k-5.7)\ge3.25k-14.62
\\\\
1.85+1.34(2.4k)+1.34(-5.7)\ge3.25k-14.62
\\\\
1.85+3.216k-7.638\ge3.25k-14.62
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
1.85+3.216k-7.638\ge3.25k-14.62
\\\\
3.216k-3.25k\ge-14.62-1.85+7.638
\\\\
-0.034k\ge-8.832
\\\\
1000(-0.034)k\ge1000(-8.832)
\\\\
-34k\ge-8832
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol) results to
\begin{array}{l}\require{cancel}
-34k\ge-8832
\\\\
\dfrac{-34k}{-34}\le\dfrac{-8832}{{-34}}
\\\\
k\le\dfrac{\cancel{2}(4416)}{\cancel{2}(17)}
\\\\
k\le\dfrac{4416}{17}
.\end{array}
