(2x+3)/5 = -(3x-2)/2 - (-3/2)(-3/2)

I've done this problem a few times and keep getting -37/38 which seems like a dumb answer to the problem. I know I think the answer should be a whole number so I don't know if that's what's confusing me. Is my answer right?

37/38 satisfies your equation, so it is correct

There is no reason to assume that an equation should have a whole number as a solution.

A number such as -37/38 is just as "good" a number as 12

thank you.

To determine if your answer is correct, we need to solve the equation and find the value of x. Let's go through the steps together:

1. Start by simplifying both sides of the equation separately.

On the left side:
(2x + 3)/5

On the right side:
-(3x - 2)/2 - (-3/2)(-3/2)

2. Simplify the right side further.

-(3x - 2)/2 + 9/4

3. Clear the fraction on the left side by multiplying both sides of the equation by 5.

5 * (2x + 3)/5 = 5 * (-(3x - 2)/2 + 9/4)

2x + 3 = -5(3x - 2)/2 + 45/4

4. Distribute the -5/2 on the right side.

2x + 3 = -(15x - 10)/2 + 45/4

5. Multiply both sides of the equation by 4 to get rid of the fraction.

4(2x + 3) = 4(-(15x - 10)/2 + 45/4)

8x + 12 = -2(15x - 10) + 45

6. Distribute the -2 on the right side.

8x + 12 = -30x + 20 + 45

7. Combine like terms.

8x + 12 = -30x + 65

8x + 30x = 65 - 12

38x = 53

8. Divide both sides of the equation by 38 to solve for x.

x = 53/38

Therefore, the solution to the equation is x = 53/38, not -37/38. It appears there might have been a calculation error.