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where are you ! 

I'm waiting !!! 

$$Notice that 40 is really the same thing as $\frac{40}{1}$\\
So now we have:\\
$\frac{3}{5} \times \frac{40}{1} = \frac{3\times40}{5\times1} = \frac{120}{5}\\$
We can reduce this fraction by dividing the top and bottom by 5\\
$\frac{120 \div5}{5\div5} = \frac{24}{1} = \mathbf{24}$$$

Suppose the question was |N| = 3

Then N could be 3 because |3| is 3, or N could be -3 because |-3| is 3.

Now replace N by 7/5x - 12.

Factoring this, we have

(10x - 1) (x + 2)  = 0

And setting each factor to 0  we have that x = 1/10  and x = -2

That kind-of makes sense. I get why you can do

(7/5x - 12) = 3

but why can you do

(7/5x - 12) = -3 ?

You lost me there...

No problem. Glad to help. :)

Thanks guys. I tried to explain it pretty well so our questioner could solve his other problems aswell.

There may be a little bit of unnecessary information. :)

Ok!so thats the main use of LCD!

i had learnt this in 6th standard and now i was wondering what lcd was when i saw that question!thanks for telling me NinjaDevo!Thumbs up!

Good, thorough explanation ND!

Well, the top number wasn't really all that important for this question, but it shows that these numbers are fractions.

Becasue the top number in a fraction is the numerator and the bottom number is the denominator.

Fining the LCD of two fractions can be usefull when you want to add or subtract the two fractions, but they don't have a common denominator.

If we wanted to just find the lowest common multiple of two non-fraction numbers, we would find the Lowest Common Multiple, or the LCM.

Does that make sense rosala?

Alan has provided an answer ND, and your answer was quite thorough.......very nice.....

In problems like this, we want to get x alone, or in other words, x = something.

We just have to manipulate this a little until we get that. The key thing to remember when changing things around is that whatever you do to one side, you have to do to the other side.

This is what we have:

 -2x-4=8x-6               ---Let's add 2x to both sides. This will "erase" the 2x from the left side.

+2x             +2x

------------------------

-4 = 8x +2x -6            

Now we can add the 8x and 2x together to get 10x. We can do this because any number times 8 + that same number times 2 = 10 times that number. To show you this, ill put in some numbers.

----------

8x+2x = 10x

8(2)+2(2)=10(2)

16+4=20

20 = 20

This a true statement, so it works. Let's try it with one more number.

8x+2x = 10x

8(9)+2(9) = 10(9)

72+18=90

90=90

Again, this is true, so we know we can do this next step I explained.

 ---------------------------

Let's do that step. 

-4 = 8x +2x -6  

-4 = 10x - 6              ---Now add 6 to both sides. The will "erase" the 6 from the right side.

+6          +6 

----------------

2 = 10x                ---We're almost there, now we just divide both sides by 10.

2/10 = x             ---Reduce the fraction on the left side.

1/5 = x

So...

x = 1/5

I see someone already answered. Hopefully my explanation can help too. :)

30 times 30 , means we are to multiply 30 by 30 so we'd do it like

30 x 30 

=900 ANSWER

-2x - 4 = 8x - 6

Add 6 to both sides  

-2x +2 = 8x

Add 2x to both sides

2 = 10x

Divide both sides by 10

2/10 = x

or x = 2/10

or x = 0.2

NinjaDevo!im still confused!why have they given the question as fractions!why cant they just give the numbers only!?

An error in the upper limit Aziz (you replaced the correct -4 with +8 in the last step!):

LCD stands for Least Common Denominator.

Here we want to find the lowest multiple of each of the denominators (bottom numbers of the fractions)

We have 5/9 and 2/3. Here are 9 and 3 multiples:

9, 18, 27, 36...etc

3, 6, 9, 12, 15, 18...etc.

Which number is the lowest but on on both lists? It looks like 9:

9, 18, 27, 36...etc

3, 6, 9, 12, 15, 18...etc.

So 9 is the LCD.

yes!me too!

anyways, thanks for the points tho!

I think there's something missing here, rosala.......this question makes no sense!!

Aziz i clicked its pic to show u!heres todays google im seeing!

And that stamp u see is India's first stamp!

i just found another link to google , check if this works!

Note that we can write r% as r/100

And a decrease of r% can be wriiten as (1 - r/100)...likewise, an increase of r% can be written as (1 + r/100)...and since the number of males and females in the class are equal after their respective decreases and increases, we have

30(1 - r/100) = 20(1 + r/100)   distribute the 30 and 20

30 - 30r/100 = 20 + 20r/100    simplify the fractions

30 - 3r/10 = 20 +2r/10          add 3r/10 to both sides....subtract 20 from both sides

10 = 5r/10

10 = 1/2r         multiply both sides by 2

20 = r

Note that if you "plug" 20 back in for r, the number of males = the number of females = 24

if your saying 2 days then obviously 48 hours it took him to deliver them!

For me its doing a superb job!and i can see the same google on phone as well!

23)

 $$log_3(2x)^2\\
=2log_3(2x)\\
=2(log_3(2)+log_3(x)) \\
=2log_3(2)+2log_3(x) \\$$

30)

$$log_29=\frac{log9}{log2}$$    And you can finish it with a calculator.

44)

$$\frac{1}{2}log_215-log_5\sqrt{75}\\\\
=\frac{1}{2}log_2(5*3)-log_5(25*3)^{1/2}\\\\
=log_2(5*3)^{1/2}-log_5(25*3)^{1/2}\\\\
=log_2(5^{1/2}*3^{1/2})-log_5(25^{1/2}*3^{1/2})\\\\
=log_2(5^{1/2}*3^{1/2})-[log_5(5*3^{1/2})]\\\\
=log_2\;5^{1/2}+log_2\;3^{1/2}-[log_5\;5+log_53^{1/2}]\\\\
=log_2\;5^{1/2}+log_2\;3^{1/2}-[1+log_53^{1/2}]\\\\
=log_2\;5^{1/2}+log_2\;3^{1/2}-\frac{2}{2}-\frac{1}{2}log_53\\\\
=\frac{1}{2} [log_2\;5+log_2\;3-2-log_53]\\\\$$

I was working this out as I was writing the code so it is probably not the best way.

Plus i am not very happy with the answer, but this is as far as I get. 

Maybe someone esle will do something more/different.  (Are you sure the base (little) numbers were correct?)