Answer
The solution set of the equation is\[\left\{ 28 \right\}\]
Work Step by Step
Consider the equation is:
$\frac{2x+1}{9}-\frac{x+4}{6}=1$
Take the LCM of the above equation:
$\begin{align}
& \frac{4\left( 2x+1 \right)-6\left( x+4 \right)}{36}=1 \\
& \frac{8x+4-6x-24}{36}=1 \\
& \frac{2x-20}{36}=1 \\
& 2x-20=36
\end{align}$
Further solve the above expression.
$\begin{align}
& 2x=56 \\
& x=\frac{56}{2} \\
& x=28
\end{align}$
Therefore, the value of $x$ is 28.
Check:
Put $\left( x=28 \right)$ in the provided equation and verify,
$\begin{align}
\frac{2\left( 28 \right)+1}{9}-\frac{28+4}{6}\overset{?}{\mathop{=}}\,1 & \\
\frac{56+1}{9}-\frac{32}{6}\overset{?}{\mathop{=}}\,1 & \\
\frac{57}{9}-\frac{32}{6}\overset{?}{\mathop{=}}\,1 & \\
\frac{19}{3}-\frac{16}{3}\overset{?}{\mathop{=}}\,1 & \\
\end{align}$
Further, simplify
$\begin{align}
\frac{19}{3}-\frac{16}{3}\overset{?}{\mathop{=}}\,1 & \\
\frac{19-16}{3}\overset{?}{\mathop{=}}\,1 & \\
\frac{3}{3}\overset{?}{\mathop{=}}\,1 & \\
1=1 & \\
\end{align}$
This is true.
Hence, the solution set of the equation is $\left\{ 28 \right\}$.
