15. w= y+z/3 ;z 16. 6x+7y=12 ;y

Question

solve each formula in terms of the given variable.

Answer 1

15.) w = y + z

                  3

First, isolate the variable you want to solve for on one side of the equation. (right now the z is tied up by addition with y on the right side). You can do this by subtracting it from both sides of the equation. It disappears from the right side and appears on the left side as a negative value. 

 

w - y = Z/3 

 

Now Z is "tied up" by division by  3 in the denominator. We need to "untie" it by performing the inverse operation of division, which is multiplication. But we have to do this to both sides of the equation. 

3(w-y) = Z 

 

Voila! now we've solved for Z 

 

16. Again, let's start by isolating the variable we want to solve for by subtracting what ever is "tied" to it on the left side of the equation. Since that's a positive 6x, we need to subtract (do the inverse operation) the 6x from both sides to get: 

7y = 12 - 6x 

 

now since y is still tied to the 7 by multiplication we have to divide to get just one y.

But you have to do this to both sides of the equation to make sure it is a balanced equation: 

y = (12 - 6x) 

          7

 

 

Answer 2

Lilac.

 

For the first equation w = y + z/3, subtract y from both sides:

 

w = y + z/3

-y    -y

 

Now we have:

 

w-y = z/3

 

Multiply each side by 3:

 

3(w-y) = 3(z/3)

 

So:

 

z = 3w - 3y

 

 

For the second equation 6x + 7y = 12, subtract 6x from both sides:

6x + 7y = 12
-6x           -6x

Now we have:

7y = 12 - 6x

Divide each side by 7:

(7y)/7 = (12 - 6x)/7

So:

y = (12/7) - (6/7)x

 

 

Answer 3

Hi Lilac,

 

You will see that both tutors gave you different answers, both of which are correct.  

 

The questions didn't specify that you simply, but you can assume that you should always simplify.  

 

In that case, Mary Ann's solution is "more correct".