IMP2 - Homework 15!

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Question Two:
In question one, you worked with a linear equation that came from the context of a real life situation. In these examples, all you have are the equations. In each case, solve the equation for the specified variable.

Solve this equation for v in terms of w.
2v + 7 = w - 3

" ...... s / r "
4r + 5s + 2 = 8r - s + 7

" ...... y / x "
5y -2x +1 = 3(y +x) - (x-5)
 
2v + 7 = w - 3

2v = w - 3 - 7

2v = w -10

v = (w-10)/2

and do the same for the others
 
2v + 7 = w - 3


To make v, the subject.


Subtract 7 from both sides.


2v = w - 10


Divide, all terms, on both sides by 2


v = w/2 - 5

Any questions about that?
 
I can do it for one, but the last two confuse me cause it has like 2 variables.

I got

4r + 5s + 2 = 8r - 5 + 7
4r = 8r - 12 + 5s + 2

&i get lost.
 
4r + 5s + 2 = 8r - s + 7

You can start by getting all the s's on one side and all the r's on the other.

Add s, to both sides:

4r + 6s + 2 = 8r + 7

Take 4r from both sides.

6s + 2 = 4r + 7

Now it is similar to the first question can you solve for the required variable?


What are you to solve for in this one?

5y -2x +1 = 3(y +x) - (x-5)

You should probably start by distributing.

5y -2x +1 = 3y + 3x - x + 5

Now you can group the variables as above.
 
5y -2x +1 = 3(y +x) - (x-5)

5y - 2x + 1 = 3y + 3x - x +5

5y - 3y +1 = 3x -x +2x + 5

2y =4x +5 -1

2y = 4x -4

y = 2x -2


or rearrange it to have x=

y-2 =2x

(y-2)/2 = x
 
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