Answer
$\left( -\infty,\dfrac{2}{5} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
7x-2(x-3)\le5(2-x)
,$ 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}
7x-2(x)-2(-3)\le5(2)+5(-x)
\\\\
7x-2x+6\le10-5x
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
7x-2x+5x\le10-6
\\\\
10x\le4
\\\\
x\le\dfrac{4}{10}
\\\\
x\le\dfrac{2}{5}
.\end{array}
Hence, the solution set is the interval $
\left( -\infty,\dfrac{2}{5} \right]
.$
