#### Answer

$x=\dfrac{1}{17}$

#### Work Step by Step

$2x-\dfrac{x}{2}+\dfrac{x+1}{4}=6x$
Multiply the whole equation by $4$, which is the least common multiple of the denominators present in the equation.
We will do this to avoid working with fractions.
$(2x-\dfrac{x}{2}+\dfrac{x+1}{4}=6x)(4)$
$8x-(4)(\dfrac{x}{2})+(4)(\dfrac{x+1}{4})=24x$
$8x-2x+x+1=24x$
Take all the terms with $x$ to the left side and take the $1$ to the right side:
$8x-2x+x-24x=-1$
Simplify:
$-17x=-1$
Solve for $x$:
$x=\dfrac{-1}{-17}=\dfrac{1}{17}$