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Isolate the variable (x) :
first move the +(1/2) to the right side resulting in :
which can be simplified to :
now move cross multiple :
   -9*(2) = -9*(x)
the -9 terms cancel leaving 
   x = 2
check by putting the result back into the original equation
Hello Jay,
Since you have a variable, x, in the denominator, you must find the least common denominator and its restriction(s).  Remember. . .what can "x" not be?  In other words, what number can never be in the denominator?  Zero.  Now let's find the least common denominator, LCD.  The LCD is 2x.
Rewrite each rational (fractional) term as an equivalent rational term with the LCD of 2x as the denominator.
x/2x - 18/2x = -8x/2x. 
Find the restriction by setting 2x = 0.  The restriction is 0. . . x cannot be zero.
Now back to solving for x. . .once all denominators are the same, then you can multiply each rational term by the LCD, 2x.  In essence you just "drop the denominator."
x - 18 = -8x.  In general, bring your terms with the variable to the left side of the equation and your constants to the right side of the equation. 
9x = 18.  x = 2, but do not forget to check your result(s).  Is 2 part of your restriction(s)?  No.   You have passed the first check, now substitute 2 back into the original equation.  Does it work?  Does -8/2 = -4?
Yes, so your answer is x = 2.