Simplifying Equations Question

Question

Hi all,

I am in the middle of a TTP question and seem to be getting stuck on particular step.

Original question stem for context 
If  x-5 = \frac{2}{3}(y-5) , and  x+10=\frac{5}{6}(y+10) , what is the value of xy?

First step:   eliminate the fraction by multiplying the entire equation by 3.

TTP says: 
 3(x-5=\frac{2}{3}(y-5)) 
 3x-15=2(y-5) 
 3x-15=2y-10 
 3x=2y+5

But why don't you multiply the  (y-5)   by 3 as well?

I was doing this: 
 3(x-5=\frac{2}{3}(y-5)) 
 3x-15=2(3y-15) 
 3x-15=6y-30 
 3x=6y-15 
 x=2y-5

Abhi077 · Answer

Here's why.

When you multiply both the equation by 3, it's like this 3 X (x - 5) = 3 X  \frac{ 2}{3}  ( y - 5), you forgot to cancel out 3. Hope this helps

WM88 · Answer

Thanks for your response  Abhi077  but why don't you distribute the 3 to (y-5)?

ScottTargetTestPrep · Answer

Hi whollymoses,

Remember, when you multiply a number through an equation you can multiply each term JUST ONCE.

So, in this case, you should see that 2/3(y - 5) is just one term.

So when you multiply the entire equation by 3, we only need to multiply 2/3 by 3 and not the rest of the parenthesis. If you were to do that you’d be changing the value of the equation.

Simplifying Equations Question

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