2x=3(x-4)=2(x-3)
How can I solve this?
You can't. Even though it is possible to string together multiple
equalities, that requires ALL of them to be equal. In this string,
the second may in fact be considered to be equal, and you could
use the first and second quantities to calculate a value for x.
However, the third quatity obviously cannot equal the first quantity.
Take those two and try to solve.
2x = 2(x-3)
2x ≠ 2x - 3
I changed the sign to an inequality, because there is no number
in existence that is equal to a number that is smaller, or larger, than
itself.
For the sake of clarity, solve the first equation formed by
the first two quantities.
2x = 3(x - 4)
2x = 3x - 12
2x - 3x = 3x - 12 - 3x
-x = -12
x = 12
If you try to use that to solve the second "equation," you
will see the obsurdity of it.
3(x - 4) = 2(x - 3)
3(12 - 4) = 2(12 - 3)
3(8) = 2(9)
24 = 18
If you believe that 24 equals 18, you are a victim of Common Core.