All Answers 358817 Answers

Then you can addd interest :)))   That is the icing on the cake :))

Yes; good to get confirmation of the result.  

However, it is probably the steps that are more important than the result for someone wanting to learn how to solve these sorts of equations!

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(4*2)+(6/3)-5=8+2-5=10-5=5.

Alan, thank you very much, you have the same result like me !

And you have written all steps !!!

Gruß radix !

Here are the steps:

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$$\begin{array}{rlll}
\frac{x-2}{2x+2}-\frac{1}{3x^2-6x-9}-\frac{x-30}{18-6x}&=&3\\\\
\frac{x-2}{2(x+1)}-\frac{1}{3(x^2-2x-3)}-\frac{x-30}{6(3-x)}&=&3\\\\
\frac{x-2}{2(x+1)}-\frac{1}{3(x-3)(x+1)}+\frac{x-30}{6(x-3)}&=&3\\\\
\frac{3(x-3)(x-2)}{3(x-3)*2(x+1)}-\frac{2*1}{2*3(x-3)(x+1)}+\frac{(x+1)(x-30)}{6(x+1)(x-3)}&=&3\\\\
3(x-3)(x-2)-2*1+(x+1)(x-30)&=&3*6(x+1)(x-3)\\\\
3(x^2-5x+6)-2+(x^2-29x-30)&=&18(x^2-2x-3)\\\\
3x^2-15x+18-2+x^2-29x-30&=&18x^2-36x-54\\\\
3x^2+x^2-15x-29x+18-2-30&=&18x^2-36x-54\\\\
4x^2-44x-14&=&18x^2-36x-54\\\\
0&=&14x^2+8x-40\\\\
0&=&7x^2+4x-20\\\\
\end{array}$$

$$\\$Now I need 2 numbers that multiply to give 7*-20=-140$\\
$and add to give +4$\\
$Obviously one will be negative and one will be positive,$\\
$The bigger one will be positive$\\
$And the absolute value difference will be 4$\\
140=7*20\\
140=7*2*2*5\\
140=14*10\\
$The numbers that we want are +14 and -10$\\
$replace 4x with 14x-10x$\\
0&=&7x^2+4x-20\\
7x^2+14x-10x-20=0\\
$Now factor in pairs$\\
7x(x+2)-10(x-2)=0\\
(7x-10)(x-2)&=&0\\
7x-10=0\quad or \quad x-2=0\\
7x=10\quad or \quad x=2\\
x=1\frac{3}{7}\quad or \quad x=2\\$$

Ofcourse you could have just used the quadratic equation to get the final answer but if you wanted to factor it than is the best way to go about it.   IMHO     

Thanks Alan for spotting my error :)

Thank you melody I understand everything now

Sorry I don't understand how you get this

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Hello sabi92,

it is too much to write, but here is the answer:

$${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{22}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{9}}\right)}} = {\mathtt{3}}$$

$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{22}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}} = {\mathtt{9}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{27}}$$

$${\mathtt{7}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{20}} = {\mathtt{0}}$$            =>    $${\mathtt{x1}} = -{\mathtt{2}}$$          ;     $${\mathtt{x2}} = {\frac{{\mathtt{10}}}{{\mathtt{7}}}}$$

Gruß radix !

Yes, i can see that Zac  

7 + (7/7) + (7*7) -7 ...... first lets get rid of the two sevens (+7 -7 = 0)

7/7 + 7*7  ............... lets simplify these terms (7/7 = 1, 7*7 = 49)

1 + 49

50

7+(7/7)+(7*7)-7=7+1+49-7=50.

It is 50, unless you made some mistake with order of operations.

Good point I did wonder if I was overcomplicating it a little. It's just how I go through it in my head.

Best forum of 2015 so far.

To be more specific, what did the anons do to you?

1680-670=1010, which is how much Jackie saves per month.

4 years= 48 months, so multiply 1010 by 48 to get your answer.

Umm... it's 482.

1960-740=1220, which is how much he saves each month.

48 months in 4 years, so just multiply 1220 by 48 to get your answer.

 8 ounces  = 1 cup      so......176 ounces =  22 cups

So  .....22cups / 32 people =    11/16 cup per person

The total length is    16 x (6 + 3/4)   =  96 + 12   = 108  meters

So   108/20   =   54/10   = 5.4 meters each

945 + 254 =  1199......   before the sale.....

1199 - 245 =  954 sold

6 1/4 - 3 1/3 - 1 2/5

Firstly, put the whole numbers back into the fraction by multiplying them by the denominator and adding that in.

(1 + (4*6))/4 - (1 + (3*3))/3 - (1 + (1*5))/5

= 25/4 - 10/3 - 6/5

Next, make all denominators the same, and multiply the numerator appropriately.

The lowest common multiple of 4, 3 and 5 is 2*2*3*5 = 60

(25*15)/60 - (10*20)/60 - (6*12)/60

= 325/60 - 200/60 - 72/60

Now make them all into a single fraction.

(325 - 200 - 72)/60

= 53/60

Since 53 is a prime number, this is the simplest form.

6 1/4 - 3 1/3 - 1 2/5 = 53/60 = 0.883 [3 recurring]

Π% = Π/100

thus Π * Π% = Π * Π / 100

= Π² / 100

= 0.09870 (Rounded to 4 s.f.)