Answer
The solution set consist of all real numbers less than or equal to $12$.
Work Step by Step
Considered the inequality,
$3\left( x+4 \right)\ge 5x-12$ ,
Apply Distributive law: $a\left( b+c \right)=ab+ac$
$\begin{align}
& 3\left( x+4 \right)\ge 5x-12 \\
& 3x+3\times 4\ge 5x-12 \\
& 3x+12\ge 5x-12
\end{align}$
Subtract $12$ and $5x$ from both sides,
$\begin{align}
& 3x+12-12-5x\ge 5x-12-12-5x \\
& -2x\ge -24
\end{align}$
Multiply both sides by $-1$ (reverse the inequality right)
$\left( -2x \right)\left( -1 \right)\le \left( -24 \right)\left( -1 \right)$
Divide both sides by $2$
$\begin{align}
& \frac{2x}{2}\le \frac{24}{2} \\
& x\le 12
\end{align}$
The solution set consist of all real numbers less than or equal to $12$.
The graph on the number line is shown below.
