How to solve 5/x - 2/3x = 17 1/3

Question

I am not sure how to solve an equation when the number after the equals sign is a combination of a whole number and a fraction. Please advise. For example, do I turn it into a fraction, so 17 1/3 would be 52/3 ? A worked example would be very helpful. Thank you.

Answer 1

5/X - 2/3X = 17 1/3

Yes, you're right; the best thing to do would be to turn 17 1/3 into the fraction 52/3.

Then the easiest way to continue is probably to multiply both sides of the equation by X:

5 - (2/3) = (52/3)X

Then put the left hand side of the equation over the same denominator:

5x(3/3) - (2/3) = (52/3)X

(5x3)/3 - (2/3) = (52/3)X

15/3 - 2/3 = (52/3)X

(15-2)/3 = (52/3)X
13/3 = (52/3)X

Then multiply both sides of the equation by 3:

13 = 52X

Then divide both sides by 52,

So,   X = 13/52

This can then be simplified:

So,   X = (13/13)/(52/13)

X = 1/4