Question 70643
{{{9*(2x-1)/7 = 4*(x-5)/3}}}
.
This is in the form of a proportion ... two fractions set equal to each other.  There are
ways that you can work through common denominators and do simplifications, but a common 
method is that a lot of students use for solving proportions that aren't way complex is 
to begin by cross-multiplying them ... multiplying the denominator on one side by the numerator 
on the other side and setting the two products equal.  For this problem the {{{7}}} would
multiply the {{{4*(x-5)}}} and the {{{3}}} would multiply the {{{9*(2x-1)}}}. You can do
that multiplication in your head and get the resulting equation:
.
{{{28*(x-5) = 27*(2x-1)}}}
.
Next do the multiplications on both sides to get:
.
{{{28x - 140 = 54x - 27}}}
.
The rest is straightforward.  Add +140 to both sides to eliminate the 140 on the left side:
.
{{{28x = 54x + 113}}}
.
Then add -54x to both sides to eliminate the 54x on the right side:
.
{{{-26x = 113}}}
.
Finally, to solve for x, just divide both sides by -26 and the answer becomes:
.
{{{x = (-113/26)}}}
.
That's the answer.  If you do the division you get a decimal answer of {{{4.346153846}}}.
.
Hope this helps you a little to see a way of working problems such as these that are in
proportional form. This method is not the only way the problem could be done, but it's 
a convenient way at times.