solve 5-2/x-6 = 10-2x/x-6?

I'm going to put in parentheses where I think they belong.

5 - (2 / (x - 6)) = 10 - (2x / (x-6))

Multiply both sides of the equation by (x - 6)

5(x - 6) - 2 = 10(x - 6) - 2x...........Multiplying we get:

5x - 30 - 2 = 10x - 60 - 2x

Group the x terms to the left hand side of the equation and the constants to the right hand side of the equation.

5x - 10x + 2x = 30 + 2 - 60

7x - 10x = 32 - 60

-3x = -28...........Multiply both sides of the equation by (-1)

3x = 28

x = 28/3 = 9.333333333.... <<<<<

If the parentheses are in the right places then this is the right answer. I'll bet my PhD in Mathematics on it.

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[23] 5 -2/(x-6)=10 -2x/(x-6) Multiplying both sides by x-6 5(x-6)-2(x-6)/(x-6)=10(x-6) -2x(x-6)/(x-6) 5x-30-2=10x-60-2x 5x-10x+2x= -60+30+2 -3x=-28 x=-28/-3=28/3=9 1/3

GERRY'S ANSWER IS RIGHT! There is confusion caused by lack of parentheses, but he has figured out where to put them. This is a MTH133 problem from Unit 3 at AIU. Way to go and THANKS a million to Gerry!!!

Presentation unclear due to lack of brackets.
Do you mean :-
5 - [ 2 / (x - 6) ] = 10 - [ 2x / (x - 6) ] ?????
5(x - 6) - 2 = 10(x - 6) - 2x
5x - 30 - 2 = 10x - 60 - 2x
5x - 32 = 8x - 60
28 = 3x
x = 28/3

PS
You will note that confusion reigns amongst answerers due to presentation of question being unclear !

(5 - 2)/(x - 6) = (10 - 2x)/(x - 6)
[x - 6][3/(x - 6)] = [x - 6][(10 - 2x)/(x - 6)]
3 = 10 - 2x
2x = 10 - 3
2x = 7
x = 7/2 (3.5)

I agree with Sethu and Junpei. The way I see it is that the 5-2 and the 10-2x is the numerator of each fraction, with x-6 being the denominator. It is correcting in stating that you can multiply both sides by x-6 which would in fact cancel both denominators of x-6 out. Leaving 5-2=10-2x.

(5-2)/(x-6) = (10-2x)/(x-6) .....(1)

multipy both side with (x-6): 3 = 10-2x .. (2)

from (2): 2x = 7
x = 3.5

-2/x + 2x/x = 4+1
-2/x + 2 = 5
-2/x = 3
-2 = 3x
x = -2/3

I am correct!!!!

here is the soln.
5-2/(x-6) = 10 - 2x/(x-6)
or,2x/(x-6)-2/(x-6) = 5
or,(2x-2)/(x-6) = 5
or,2x-2 = 5x-30
or,3x = 28
so, x = 28/3.

sethu is wrong , I'm afraid....

(5-2)/(x-6) = (10-2x)/(x-6)

Cancel (x-6) on both sides, assuming x not equal to 6.

That is, 5-2 = 10-2x
or 2x = 10-3
or x = 3.5