Problem with basic explanation of algebra problem

• January 1st 2014, 10:37 AM
bkruss
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.
• January 1st 2014, 11:14 AM
Plato
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: $\dfrac{2(8-2y)}{4}-y=-2$.

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

$2(8-2y)-4y=-8$. The 2 is in the numerator, the 4 is in denominator and divides off.
• January 1st 2014, 11:46 AM
HallsofIvy
Re: Problem with basic explanation of algebra problem
Alternatively, 4 times both slides of $\dfrac{2(8- 2y)}{4}- y= 2$ is $\frac{8(8- 2y)}{4}- 4y= -8$ so there is an "8" in front, in the numerator. But, of course, $\dfrac{8}{4}= 2$.