Okay, so I need to solve the equation (x/2) + (x/3) = 5. Hmm, let me think. Alright, first, I remember that when you have fractions like this, a common way to solve for x is to find a common denominator. Let me check, the denominators here are 2 and 3. The least common denominator for 2 and 3 is 6, right? So maybe I can multiply both sides of the equation by 6 to eliminate the fractions. That should make it easier to handle. Let me try that.

Multiplying both sides by 6: 6*(x/2) + 6*(x/3) = 6*5. Let's compute each term. For the first term, 6 divided by 2 is 3, so 3x. The second term, 6 divided by 3 is 2, so 2x. The right side is 30. So now the equation becomes 3x + 2x = 30. Combining like terms, 3x + 2x is 5x. So 5x = 30. To solve for x, divide both sides by 5. That gives x = 30/5 = 6. Let me check if that works. Plugging x = 6 back into the original equation: (6/2) + (6/3) = 3 + 2 = 5. Yep, that's correct. So x = 6 is the solution. But wait, let me make sure there's no other way this could be approached. Maybe using a different method to confirm.

Alternatively, I could combine the fractions first. The equation is (x/2) + (x/3) = 5. To add these fractions, they need a common denominator. As before, the LCD is 6. So, converting each fraction: (x/2) is equivalent to (3x/6), and (x/3) is equivalent to (2x/6). Adding those together gives (3x + 2x)/6 = 5x/6. So the equation becomes 5x/6 = 5. To solve for x, multiply both sides by 6: 5x = 30, then x = 6. Same result. Good, so both methods lead to the same answer. I think that's solid. I don't see any mistakes here. Maybe another check: if x were 5, then (5/2) + (5/3) = 2.5 + 1.666... ≈ 4.166..., which is less than 5. If x were 7, then 3.5 + 2.333... ≈ 5.833..., which is more than 5. So 6 seems right in between, giving exactly 5. Yep, that makes sense. So I'm confident the answer is 6.
</think>