Answer
$x\le-4a$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the order of operations and the properties of inequality to solve the given inequality, $
-(x+5)\ge4a-5
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-(x+5)\ge4a-5
\\\\
-1(x)-1(5)\ge4a-5
\\\\
-x-5\ge4a-5
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-x-5\ge4a-5
\\\\
-x\ge4a-5+5
\\\\
-x\ge4a
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-x\ge4a
\\\\
\dfrac{-x}{-1}\ge\dfrac{4a}{-1}
\\\\
x\le-4a
.\end{array}
