Melody

Sounds like a plan     

Quilly don't be lazy.

Type your question in.

For hard to write question you can learn to use the  insert image button but it is easier for answerers if you type your question in.

This question would be easy for you to type in.

Hint:

Start by multiplying both sides by -2  but remember that when you multiply by a negative number you must turn the inequality around. so the  <  will become >

This is the question

Thanks Rom,

Would it be fair to say that the fallacy in my answer is that i assumed such an x existed in the first place ?

the members of the ecology club collected 3500 empty aluminum cans to take recycling center.

if 21 cans make 1.0 pound of aluminum

how many liters of aluminum are obtained from the cans? (1 kg = 2.20 pounds) , (density of aluminum 2.70 kg/m^3)

3500 cans, 

\(\frac{21 cans}{1.0 lbs}\qquad \frac{1kg}{2.2lbs}\qquad \frac{2.7kg}{m^3}\qquad \frac{1000L}{m^3}\qquad \qquad find\;\;L\\ \\~\\ \frac{1000L}{m^3}\times \frac{1m^3}{2.7kg}\times \frac{1kg}{2.2lbs} \times \frac{1.0 lbs}{21 cans}\times \frac{3500cans}{1}\\~\\ =\frac{1000*1*1*1*3500L}{1*2.7*2.2*21*1}\\ =\frac{1000*3500L}{2.7*2.2*21}\\ =\frac{50000000}{27*22*3}L\\ \approx 28\;058.4L\)

Hi Mellie,

It is great to see you again   

Given a rough inspection I think they are all the same sort of factorization.

So if I do the first one and you understand then you are capable of doing the other three yourself.

9)     

 \(4r^3-8r^2-5r+10\\ =4r^3-8r^2\qquad\qquad -5r+10\\ \text{now factorize the pairs}\\ =4r^2(r-2)\qquad\qquad -5(r-2)\\\)

now you can think of (r-2) as just one thing.

So you have  \(4r^2\)  lots of (r-2)   and then you take away  \(5\) lots of (r-2)

That will give you   \((4r^2-5)\)    lots of   (r-2)

which is

\((4r^2-5)(r-2)\)

you could take this one step further by treating \(4r^2-5\) as the difference of 2 squares

\(4r^2 = (2r)^2 \)     and      \(5=(\sqrt5)^2 \)    so

\((4r^2-5) = (2r-\sqrt5)(2r+\sqrt5)\)

\((4r^2-5)(r-2)=(2r-\sqrt5)(2r+\sqrt5)(r-2)\)

The question is incomplete.