To solve the equation |x-3|=2x-9, we can split it into two separate equations:

1) x-3 = 2x-9
2) -(x-3) = 2x-9

Let's solve each equation separately:

1) x-3 = 2x-9

First, let's simplify the equation by combining like terms:

x - 2x = -9 + 3
-x = -6

Next, let's isolate x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-6)
x = 6

So, x = 6 is one solution to the equation.

2) -(x-3) = 2x-9

First, let's simplify the equation by distributing the negative sign:

-x + 3 = 2x - 9

Next, let's combine like terms:

-x - 2x = -9 - 3
-3x = -12

Now, let's isolate x by dividing both sides of the equation by -3:

(-3x)/(-3) = (-12)/(-3)
x = 4

So, x = 4 is another solution to the equation.

Therefore, the equation |x-3|=2x-9 has two solutions: x = 6 and x = 4.