Question 169773
{{{(7x/4)-((6x-(1))/2)=(3/4)}}}


Just multiply the {{{(6x-(1))/2}}} part by 1 in the form of {{{2/2}}} so that all of the denominators are the same, namely 4:


{{{((6x-(1))/2)(2/2)=(12x-2)/4}}} so that


{{{(7x/4)-((6x-(1))/2)=(3/4)}}} (your original problem) becomes:


{{{(7x/4)-((12x-2)/4)=(3/4)}}}


Now you can collect like terms in the numerators (because you can just add numerators anytime the denominators are equal).


{{{(-5x+2)/4=3/4}}}


Multiply both sides of the equation by 4


{{{-5x+2=3}}}


Add -2 to both sides


{{{-5x=1}}}


And finally divide both sides by -5


{{{x=-(1/5)}}}


Check the answer by substituting {{{-(1/5)}}} for {{{x}}} in the original equation and do the arithmetic to see if a true statement results.  I'll leave this part as an exercise for the student.