What Are The Steps To Solve 3/4x-5=2/3x?

The first step is to make sure you have the equation right.

Here is what I think you want;

(3/4)x - 5 = (2/3) x

If this is correct, we would proceed by finding a common denominator.  I'd go with 12, because it's 4 x 3, from the existing denominators.

In order to make 3/4 into something over 12, you would multiply both top and bottom by 3.  In this case you would have 9/12.

In the other case you need to make 2/3 into something over 12, you would multiply both top and bottom by 4.  So you would end up with 8/12.

But what about the integer 5?  We probably need it to be something over 12 as well, so let's multiply 5 by 12 and get 60/12

So replace all these into the equation.

(9/12)x - (60/12) = (8/12)x

Now we can rewrite that as:

9x - 60 = 8x
    12       12

so we can subtract 8x from the numerators on each side to get a simpler equation

x - 60 = 0    
   12

then add 60/12 to each side... And you're almost done

x/12 = 60/12

multiply both sides by 12 to simplify

x = 60


There are other ways to end up with the same result.  We could have subtracted the 8x earlier.  But if your algebra is correct you still end up with the same result.  There's one last step that you should do, substitute 60 into your original equation to check it.  If it doesn't check, you (or I!) made a mistake.

(3/4)60 - 5 = (2/3) 60

180/4 - 5 = 120/3

45 - 5 = 40

so it checks!


Have a great day