Help with isolating variables

[amartino44]

Hello. It's been a while since I've done math haha How do you solve for x and y here? (x-y)/10 = (x+y)/14? The answer is x=6y but I don't see how that is. Wouldn't you multiply the right side of the equation by 10? So that would be (10x + 10y)/14? Help!!

 

[Deleted member 4993]

Hello. It's been a while since I've done math haha How do you solve for x and y here? (x-y)/10 = (x+y)/14? The answer is x=6y but I don't see how that is. Wouldn't you multiply the right side of the equation by 10? So that would be (10x + 10y)/14? Help!!

The process is to multiply both sides by the LCM of the denominators.............. edit

The denominators are 10 & 14 - their LCM is 70............... edit

Then multiply BOTH sides of the equation by 70 - to get:

7 * (x - y) = (x + y) * 5

Now simplify....

 

[lookagain]

The process is to multiply both sides by the GCD of the denominators.

The denominators are 10 & 14 - > > > their GCD is 70. < < < No.

Then multiply BOTH sides of the equation by 70 - to get:

7 * (x - y) = (x + y) * 5

Now simplify....

No, the GCD, which is the greatest common divisor, and the GCF, which is the greatest common factor,
are both equal to 2.

The LCD is the least common denominator, and that is what you want, is equal to 70.

 

[Deleted member 4993]

No, the GCD, which is the greatest common divisor, and the GCF, which is the greatest common factor,
are both equal to 2.

The LCD is the least common denominator, and that is what you want, is equal to 70.

I stand corrected and corrected my post......

 

[amartino44]

thanks

Got it. Thank you all.