Melody

12x+8*3/4x=4176

\(12x+8*\frac{3}{4}x=4176\\\\ 12x+2*\frac{3x}{1}=4176\\\\ 12x+6x=4176\\\\ 18x=4176\\\\ 18x/18 = 4176/18\\\\ x=232 \)

If you take cold (negative) air out of a room then the room gets warmer.

so  - - = +

-8 - - 6 = -8 + 6 = -2

You have made a small error

2(x-10)+1=60

2x-20 +1 =60

2x  -19 = 60

2x        = 79

x=  79/2 

x=39.5

now 0.5 = 1/2   so

39.5 = 39 and a 1/2

The fraction part of the calc may not be working properly but you do not need a calc for this :)

Do you mean    \(\frac{738}{2+4} \;=\;\frac{738}{6}\;=\;123\)

Yes, a log is a power or an exponent

10^2=100

so

\(log _{10}100 = 2\)

This is read as log of 100 base 10 =2

If there is no base written log would be assumed to be base 10  :)

Look at this great taxi i saw today :)

https://gyazo.com/78e030e2e4ee24ca9e83cd7cb966f07f

https://gyazo.com/6945212057dc333f569a628077765539

I had just been to the Museum of History and Science where I had learned a little about Henry Moseley.

So seeing this car was just wonderful.

I was in a double decker bus when I took the shot.  I was sitting up the top right at the very front.   :)

Henry Moseley

https://www.google.co.uk/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=Henry+Moseley

It is really nice to meet you Emurry.

It is great when students demonstrate an active interest in learning from other people's answers :)

Emurry, I was just looking at your answer. :)

1-y<|2x-1|

-y < -1 + |2x-1|

y > 1 - |2x-1|

this is different from your version.

-|2x-1|  is not equal to |-2x+1|

If you think about it for a moment you will realise that the first expression is negative and the second one is positive. :)

1-y<|2x-1|

-(2x-1) < 1-y < 2x-1

-2x+1 < 1-y < 2x-1

-2x+1 -1 < 1-y -1 < 2x-1 -1

-2x < -y < 2x- 2

-2x < -y      and       -y < 2x- 2

2x > y      and       y > -2x+ 2

y<2x       and        -2x+ 2 < y

-2x+2 < y < 2x

This also means that  

-2x+2<2x

2 < 4x

1/2 < x

x > 0.5

I have not checked this answer - if you have questions please ask.

I have been busy doing this assuming that     i = sqrt(-1)

BUT

looking at it this looks like a compund interest question, so our answering guest is correct, you probably need to give us the value of i  (interest rate per compounding period.)

Thanks guest.  :)