The sum of a number and 6 times its reciprocal is 5. Find the number(s).

Question

anonymous · Answer

Write this as an equation, where the number = x

anonymous · Answer

im not good at writing equations @IvoryKnight

anonymous · Answer

You are going to need to learn if you are going to get anywhere in math.
At the higher levels, everything is an equation.
Ok lets look at this one number at a time, on one side, you are adding a number and 5 times that number's reciprocal. On the other side, you have 5. Try writing out the equation, if you make a mistake, I will at least know what direction to point you in.

anonymous · Answer

As a general tip, "sum", always means "put in a plus sign" and "is" always means "="

anonymous · Answer

6x+5=x

shayaan_mustafa · Answer

Hi tbrooks3 :)

How are you dear? :)

shayaan_mustafa · Answer

Let us take the required number as "x"

anonymous · Answer

hi im fine, thanks for asking. how r u?

shayaan_mustafa · Answer

The sum of a number and 6 times its reciprocal is 5.

The sum of a number and 6 times its reciprocal = 5

The sum of "x" and 6 times "1/x" = 5

The x + 6(1/x) = 5

Finally,

$$\Large x+\frac{6}{x}=5$$

shayaan_mustafa · Answer

I am fine too :)

shayaan_mustafa · Answer

Have you got how did I get the equation?

anonymous · Answer

yes i solved it and recieved the 2 solutions (2,3)... thanks alot :)

shayaan_mustafa · Answer

Yes great.. Ever welcome.

anonymous · Answer

@Shayaan_Mustafa if i want to find A number minus 20 times its reciprocal is 1. would the equation be $$x -\left(\begin{matrix}20 \ x\end{matrix}\right)=1$$

anonymous · Answer

Yes, exactly.

anonymous · Answer

thanks

shayaan_mustafa · Answer

Yes. You got it. Now I can say my labor worked. lol

anonymous · Answer

lol :)

anonymous · Answer

im stuck again . would i just do $$50\div7$$ for the sum of an integer and its reciprocal is 50/7. Find the integer.

shayaan_mustafa · Answer

Let say that required integer is "x"

The sum of an integer and its reciprocal is 50/7

The sum of an integer and its reciprocal = 50/7

The sum of "x" and "1/x" = 50/7

x + 1/x = 50/7

Finally,

$$\Large x+\frac{1}{x}=\frac{50}{7}$$

anonymous · Answer

ohh okay thanks

shayaan_mustafa · Answer

My pleasure :D

anonymous · Answer

could the solution be $$\left(\begin{matrix}1 \ 7\end{matrix}\right) , 7$$

anonymous · Answer

or would i simplify the fraction?

shayaan_mustafa · Answer

You can check your answer by substituting each in the given equation. 
And if your answer is right then right hand side and left hand side of the equation will be same.