#### Answer

$x=-\dfrac{3}{4}$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
4x-(x+6)=5(3x-1)+8
$, is
\begin{array}{l}
4x-x-6=15x-5+8
\\\\
3x-6=15x+3
\\\\
3x-15x=3+6
\\\\
-12x=9
\\\\
x=\dfrac{9}{-12}
\\\\
x=-\dfrac{3}{4}
.\end{array}
CHECKING:
\begin{array}{l}
4\left( -\dfrac{3}{4} \right)-\left(-\dfrac{3}{4}+6 \right)=5\left(3\left( -\dfrac{3}{4} \right)-1\right)+8
\\\\
-3-\left(-\dfrac{3}{4}+\dfrac{24}{4} \right)=5\left(-\dfrac{9}{4}-\dfrac{4}{4}\right)+8
\\\\
-3-\dfrac{21}{4}=5\left(-\dfrac{13}{4}\right)+8
\\\\
-\dfrac{12}{4}-\dfrac{21}{4}=-\dfrac{65}{4}+\dfrac{32}{4}
\\\\
-\dfrac{33}{4}=-\dfrac{33}{4}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=-\dfrac{3}{4}
$.