9/5(3-x)=3/4(x-3)? How do you solve this? is the L.C.M. 20?

9/5(3-x)=3/4(x-3) lcm:20
36(3-x)=15(x-3)
108-36x=15x-45
-36x-15x=-45-108
-51x=-153
x=3 answer//

Incorrectly presented.
Should be clearly shown as :-

(9/5) ( 3 - x ) = (3/4) ( x - 3 )

36 ( 3 - x ) = 15 ( x - 3 )

108 - 36 x = 15 x - 45

153 = 51 x

x = 3

5 & 4 have not common factor, so LCM = 5 x 4 = 20
9/5(3-x)=3/4(x-3)
factor out -1 from (x -3)
9/5(3-x)=3/- 4(3- x)
9/5(3-x) + 3/4(3-x) = 0

9/5(3 - x) = 3/4(x - 3)
27/5 - 9/5x = 3/4x - 9/4
- 9/5x - 3/4x = - 27/5 - 9/4
- 36/20x - 15/20x = - 108/20 - 45/20
- 51/20x = - 153/20
(20/51)-51/20x = (20/51)-153/20
- x = - 3
or
x = 3.

9/5(3 - x) = 3/4(x - 3)
[9(3 - x)]/5 = [3(x - 3)]/4
(27 - 9x)/5 = (3x - 9)/4
4(27 - 9x) = 5(3x - 9)
108 - 36x = 15x - 45
-15x - 36x = -108 - 45
-51x = -153
x = -153/-51
x = 3

x= 3

Here's a more creative approach:
Factor a (-1) out of the left parenthesis. You get -9/5 (x-3) = 3/4 (x-3)
Clearly -9/5 never equals 3/4.
Therefore (x-3) must equal zero.
Then we have x=3.
You can check it in the original equation, and you have 0=0, which is true.

The LCM of the denominators is 20, since 5 and 4 have no common factors. Let's multiply both sides by 20:

20* 9/5(3-x)= 20* 3/4(x-3)

Using cross canceling on the fractions, we get

36(3-x) = 15(x-3).

Now, use the distributive property on each side:

36 * 3 - 36x = 15x - 15 * 3

108 -36x = 15x -45.

To solve for x, we need to get all the x's on one side of the equation. The most convenient way is to add 36x to both sides:

108 = (15x - 45) + 36x
or
108 = 51 x - 45.

Now, this is easy; add 45 to both sides:

153 = 51 x

and divide both sides by 51:

x = 3.

You can use lcm

36/20(3-x) = 15/20(x-3)

multiply bs by 20
36(3-x) = 15(x-3) = -15(3-x) Can you guess what is coming?



(36+15)(3-x) = 0
51(3-x) = 0

so 3-x must equal 0, x=3