#### Answer

$x\ge-1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
2x+6\le5x+9
,$ use the properties of inequality to isolate the variable. Then, graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
2x+6\le5x+9
\\\\
2x-5x\le9-6
\\\\
-3x\le3
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign) results to
\begin{array}{l}\require{cancel}
-3x\le3
\\\\
\dfrac{-3x}{-3}\ge\dfrac{3}{-3}
\\\\
x\ge-1
.\end{array}