Part A: Solve A = 9 over 2(x + 28) for x.
Part B: Determine the value of x when A = 135.
Part C: Solve –np – 40 > 10 for n. Show your work.

- anonymous

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- anonymous

\[A= \frac{ 9 }{ 2 } \left( x + 28\right)\]

- anonymous

@zepdrix can you help me with this?

- Vocaloid

part A: "solve for x" means we want to get x by itself
start by multiplying both sides of the equation by 2 to eliminate the denominator

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## More answers

- anonymous

A2=? (x + 28)

- zepdrix

\[\large\rm A=\frac{9}{2}\left(x+28\right)\]Multiplying both sides by 2 gives you,\[\large\rm 2\cdot A=2\cdot\frac{9}{2}\left(x+28\right)\]Don't think of that 2 as a denominator, think of the operation being performed.
It's actually division by 2.
So we're multiplying and dividing by 2 on the right side of the equation.
Those actions will "cancel out".\[\large\rm 2\cdot A=\cancel{2}\cdot\frac{9}{\cancel{2}}\left(x+28\right)\]

- zepdrix

Which puts you here,\[\large\rm 2A=9(x+28)\]

- anonymous

divide by 9 and then subtract 28? @zepdrix

- anonymous

\[\frac{ A2 }{ 9 }-28=x\]

- zepdrix

Ahh sorry had to go make some food +_+

- zepdrix

Looks good!

- anonymous

2! the answer to B it x = 2!

- zepdrix

yay good job \c:/

- anonymous

:DD

- anonymous

-np - 40 > 10
add 40 first or...

- zepdrix

Yah, that seems like a good first step

- anonymous

-n > 50/p
but what about that minus sign?

- zepdrix

I guess you'll want to divide each side by -p, not simply p.
Do you remember what happens when you divide a negative across an inequality?

- anonymous

the inequality flips

- zepdrix

yessss

- anonymous

n < 50/-p

- zepdrix

Ok great!
Let's bring the negative sign out front because
\(\large\rm \frac{50}{-p}\) is the same as \(\large\rm \frac{-50}{p}\) which is the same as \(\large\rm -\frac{50}{p}\).
It doesn't really matter where the negative goes, it just looks nicer in front like this form.

- anonymous

ok. do you have time for one more question?

- zepdrix

sure!

- anonymous

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.
Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation.
Part B: How many liters of lemon juice are present in the bottle? Show your work.
This one is really confusing to me.

- zepdrix

Mmm I remember this one coming up like 6 months ago, confused me also lol
gimme a sec XD

- anonymous

ok :)

- anonymous

im not so smart

- zepdrix

Oh oh oh oh oh.. ok now I remember why I got confused on this one.
Make sure you understand the second sentence.
It's NOT saying that bottle contains 1Liter of liquid.
It contains 1Liter of water. They're not telling us how much total liquid is in the bottle.

- zepdrix

So umm

- anonymous

Ok, i see how that can get you!

- zepdrix

Ok if lemon juice accounts for 60% of the liquid in the bottle,
what % does that leave for water?

- anonymous

40%

- zepdrix

Good good good. and I think we can use thattttt :)
sec, brain ... not... working lol

- anonymous

lol

- zepdrix

The `amount` of water is 1Liter.
So this 1Liter accounts for 40% of the total Liquid in the bottle.
\(\large\rm 1L=.40T\)
So how much total liquid is in the bottle?
Can you solve this algebraically? (Ignore the L, that's just a unit).

- anonymous

Darude-Sandstorm

- anonymous

1.40L

- anonymous

t

- zepdrix

Woops! The 40% is `multiplying` the Total.
So to isoluate your total, T, you'll need to divide.

- zepdrix

isolate*

- anonymous

2.5

- zepdrix

Good good good.
We've determined that the total amount of liquid in the bottle is 2.5Liters.
The lemon juice accounts fo 60% of that total.
So we can again set this up algebraically:\[\large\rm \ell=.60T\]And since we've solved for the total, T, we can plug it right in,\[\large\rm \ell=.60\cdot 2.5\]And solve for l, the amount of lemon juice in the bottle.

- zepdrix

Do those steps.... kinda make sense? 0_o
It's a tricky problem to get through.

- anonymous

1.5

- anonymous

1.5=.60*2.5

- zepdrix

Good! :)
So there is:
1Liter of water which is 40% of the total liquid
1.5Liter of lemon juice which is 60% of the total liquid
2.5Liters of total liquid which is 1 + 1.5

- zepdrix

Yayyy I think we did it \c:/

- anonymous

Thank you so much for all your help today! I really understand it better too.

- zepdrix

np \c:/ yay team!

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