Problem with basic explanation of algebra problem

So here's the problem. 2 X (8-2y/4) -y =-2. The author says that he simplifies the equation by adding 4 to both sides and gets this 2 x (8-2y) -4y = -8. So, my question is why is the 2 in the front not an 8? i.e, 8 x (8-2y) - 4y= -8.

Thanks for the help.

Re: Problem with basic explanation of algebra problem

Quote:

Originally Posted by

**bkruss** So here's the problem. 2 X (8-2y/4) -y =-2. The author says that he simplifies the equation by adding 4 to both sides and gets this 2 x (8-2y) -4y = -8. So, my question is why is the 2 in the front not an 8? i.e, 8 x (8-2y) - 4y= -8.

First, write it correctly: $\displaystyle \dfrac{2(8-2y)}{4}-y=-2$.

Now I hope he/she said **multiply** both sides by 4. **NOT **__ADD__.

$\displaystyle 2(8-2y)-4y=-8$. The 2 is in the numerator, the 4 is in denominator and divides off.

Re: Problem with basic explanation of algebra problem

Alternatively, 4 times both slides of $\displaystyle \dfrac{2(8- 2y)}{4}- y= 2$ is $\displaystyle \frac{8(8- 2y)}{4}- 4y= -8$ so there is an "8" in front, in the numerator. But, of course, $\displaystyle \dfrac{8}{4}= 2$.