Okay, so I need to solve the equation 2/3 = 4/(x-5) for x. Let me think about how to approach this. Hmm, solving equations with fractions can sometimes be tricky, but I remember that cross-multiplying is a common method. Let me try that.

First, the equation is 2/3 = 4/(x-5). If I cross-multiply, that should eliminate the denominators. So, multiplying the numerator of the left side by the denominator of the right side and vice versa. That would give me 2*(x-5) = 3*4. Let me check that again to make sure I didn't mix up the terms. Yes, left numerator times right denominator equals right numerator times left denominator. So that part seems right.

Now, simplifying both sides. On the left side, 2*(x-5) becomes 2x - 10. On the right side, 3*4 is 12. So now the equation is 2x - 10 = 12. To solve for x, I need to isolate x. Let me add 10 to both sides first. That would give 2x = 12 + 10, which is 22. Then, divide both sides by 2, so x = 22/2, which simplifies to x = 11.

Wait, let me verify that. If I plug x = 11 back into the original equation, does it hold true? Let's check. The right side becomes 4/(11-5) = 4/6 = 2/3. And the left side is 2/3. Yes, that works. So x = 11 is the correct solution.

But wait, let me make sure there's no other possible solution or if there's a restriction on x. The original equation has a denominator x-5, so x can't be 5 because that would make the denominator zero, which is undefined. But since our solution is 11, which is not 5, that's fine. So no issues there.

Alternatively, maybe I can solve it another way to confirm. Let's see. Starting with 2/3 = 4/(x-5). Maybe I can write 4 as 2*2, so 4/(x-5) is the same as 2*2/(x-5). Then, comparing to 2/3, maybe set 2/(x-5) equal to 2/3? Wait, no, that's not right because 4/(x-5) is 2*2/(x-5), which is different from 2/(x-5). Hmm, maybe that's a wrong approach.

Alternatively, maybe take reciprocal on both sides? If I take reciprocal of both sides, that would give 3/2 = (x-5)/4. Then multiplying both sides by 4 gives (3/2)*4 = x - 5. Which is 6 = x -5, so x = 11. Same result. That's another way to verify. So both methods give x = 11, which is consistent.

Another check: maybe using decimal equivalents. 2/3 is approximately 0.666..., and 4/(x-5) should be the same. If x =11, then x-5=6, so 4/6=0.666..., which matches. So that's correct.

I think that's thorough enough. The solution seems solid, and both methods confirm the same answer. No mistakes detected in the process. So I can confidently say x = 11 is the solution.
Therefore, the solution to the equation is $x = \boxed{11}$.
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