Algebra homework. Please help!?

Question

Alright so I have this dumb algebra homework. I missed the day of the lesson so I have absolutely no clue what's going on. Here's a few questions, and maybe you can help me out :]

w= 3m - 4k
(solve for k)

I = p(1 + r)
(solve for r)

Answer 1

First of all, when you manipulate a formula you have to be aware that if you add something at the right of the = sign, you must do the same at the other side.

For the first equation, you have to solve for k, this is, leave k alone. To do this, you first see where is the k. Here,
w = 3m - 4k

What I will do first is to put the -4k positive. To do this, sum 4k in both sides. This is:

4k + w = 3m - 4k +4k

So, remember to sum "bottles with bottles" and "snakes with snakes". 3m - 4k + 4k gives 3m, because you are adding -4k +4k which gives 0. Cool? Ok.

Then, the equation is like this:

4k + w = 3m

Then, to isolate the 4k, you have to do the same with the w:

4k + w - w = 3m - w

I am subtracting w at both sides of the equation. Then,

4k = 3m - w right? Ok.

Now we have to multiply by 1/4 at both sides, because we have to leave the k alone with no 4. So,

(1/4) 4k = (1/4) (3m - w)

The 4 in 4k equals 1 when we divide it by 4... Don't get lost!! Let's see:
(1/4) multiplied by 4 is 1 right? Got it? Ok.

Now, our equation gives:

k = (3m - w)/4

Let's go for the other one. Here you have to solve for r, and r is inside something. You have to get r out and isolate it in order to solve for it. So,

l = p (1 + r)

Let's multiply the right part of the equation by p:

this is, l = p (1) + p (r) Got it? Ok

then, .l = p + pr right?

Now, as in the other equation, you have to leave the r alone. I will "move" p to the other side:
l - p = p - p + pr
l - p = pr

Then, this is the same as in our first equation. You have to divide in both sides by p, or multiply by 1/p if you want to see it this way.

This is:

(1/p) (l - p) = (1/p) pr

So, (1/p) (pr) gives r, remember that (1/p) p is 1 right? Don't get lost!! This is the very same exercise as the first one, but with letters instead of numbers.

Then, [(l - p) / p ] = r

or r = (l - p) / p

TADA!!!

Remember that in every problem you have to see where is the variable you are going to isolate. If it is inside something, you have to get it "out" first and then isolate. And to isolate, you have to multiply, divide, add or substract at both sides of the equation. Having this in mind, everything should be "smooth". And, must of all, remember to practice every day.

Hope this helps

Answer 2

1. w= 3m-4k You subtract 3m from both sides, 3m cancels out
-3m -3m leaving you with w-3m=4k.

w-3m=4k Divide 4 from w-3m and from 4k. 4 cancels out leaving you with k=w-3m divided by 4(looks like k = w-3m with aline under and a 4)

Now you must check.

w= 3m-4k

w=3m-4(w-3m divided by 4) The four on the outside and inside of the parenthesis cancel each other out.

you are left with:

w= 3m-(w-3m) 3m cancel each other out. (the 3m on the outside is positive and the 3m inside the parenthesis is negative, neg. & pos. cancel each other out, you get a negative.)

so w=w. Always remember to check after solving.


2. I = p(1+r)

divide 1 from both sides 1(they cancel out) and I.
Leaves you with:

I/1 (I divided by 1) = p+r


I/1= p+r subtract p to both sides, p's cancel out, leaving you
-p -p
with I-p with a line underneath and 1 (I-p divided by 1)



Now check: I= p(1+r)
substitute. I=p(1+(I-p/1)) Divided by 1 (looks like I-p with a line under and 1) 1 and 1 cancel out (1 divided by 1.)

You are left with:I= p+(I-p) p's cancel out (division)

I-I Your done, I hope I could make it clear enough for you, and study!!

Answer 3

your just spposed to get k and r to equal the other variables right?

w=3m-4k
w-3m= -4k
w - 3m/-4=k

l=p(1+r)
l=1p+pr
l/p=1+r
(l/P) + 1 = r

Answer 4

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Answer 5

w=3m-4k
subtract 3m from both sides
w-3m=-4k
divide both sides by -4
(w-3m)/-4=k

I=p(1+r)
divide both sides by p
I/p=1+r
subtract one from both sides
(I/p)-1=r

Answer 6

w=3m-4k
w+4k=3m
4k=3m-w
k=(3m-w)/4


l=p(1+r)
l=(p*1) + (p*r)
l=p+pr
l-p=pr
r=(l-p)/p