Question

Which answer is correct?

Question: Solve for d.
\[c=\frac{ r(4-d) }{ y }\]


ANSWER1:
\[d=\frac{ -cy+4r }{ r }\]


or mathways answer: ANSWER2:

\[d=4-\frac{ cy }{ r }\]

Answer 1

-4r / -r = 4
and
we also have cy / -r = -cy/r

Answer 2

4 - cy
--
r

Answer 3

I'm slightly confused

Answer 4

both answer1 and answer2 are correct.

You do not see how to change from one version to the other ?

Answer 5

do you know which the professor will accept?

Answer 6

both are correct.
If I were the teacher, I would accept the one you got on your own.
If you can't explain it, then I would not accept either.

The idea is not to get the answer, the idea is to know how to get the answer.

Answer 7

For example, when you look at
\[ c=\frac{ r(4-d) }{ y } \]
you see the "d" is buried in parens on the right side and it looks messy

But you could (should) say, "I can get rid of the y by multiplying both sides by y"
that is because you know that y/y is 1

so you would do this
\[ c\cdot y = \frac{r(4-d)}{\cancel{y}} \cdot \cancel{y}\]

Answer 8

we don't usually bother to show the multiply sign (usually a "dot") if we multiply two "letters"
so you have
\[ cy = r(4-d) \]

Answer 9

you should now think: If I could get rid of the r, that would be progress.
if I divide r by r I get 1, and multiplying by 1 can be ignored.

But if I divide by r on the right side, I have to do the same on the left side.

Answer 10

so you do this
\[ \frac{cy}{r} = \frac{r}{r} (4-d) \]

Answer 11

on the right side r/r is 1 and 1 times (4-d) is (4-d)
so now it is
\[ \frac{cy}{r}= 4-d \]
we can drop the parens because they are not doing anything.

Answer 12

if you add -4 to both sides like this
\[ \frac{cy}{r}-4 = 4-4 -d \]
and simplify 4-4 to 0, and 0-d is just -d
\[ \frac{cy}{r}-4 = -d \]
that is almost d all by itself.

Answer 13

to change -d to +d, you can multiply it by -1
because -1*-d is d
and you have to do the same thing to the other side
(which means multiply *everything* on the left by -1
you get
\[ -1\cdot \frac{cy}{r} + -1\cdot -4 = d \\
d= -\frac{cy}{r} + 4 \]
or, to make it look nicer, we can change the order
\[ d = 4 -\frac{cy}{r}\]