Question 237623
There might be an easier way to solve this, but I found a way to do it.
First, build the equation.
The sum of 
one-half of a number... 1/2x
one third of the number... 1/3x 
and one-fourth of the same number... 1/4x 
is one-tenth... = 1/10
{{{(1/2)x+(1/3)x+(1/4)x=1/10}}}
Now mulitiply entire equation by the LCD...
I multiplied 2x3x4=24, so I used 24
{{{24((1/2)x+(1/3)x+(1/4)x)=24*(1/10)}}}
{{{12x+8x+6x=(24/10)}}}
{{{26x=(24/10)}}}
Now divide 26 from both sides
(this is the same as multiplying by its reciprocal... 1/26), so
{{{x=(24/10)*(1/26)}}}
{{{x=24/260}}}
You may now simplify the fraction to a simpler fraction.
I'll let you work on that step, since it's the last one.  :)