I'm happy to help you with this equation! Let's solve it step by step using the properties of equality:
1. Start by multiplying both sides of the equation by the least common denominator of the fractions to get rid of the fractions. In this case, the least common denominator is 6.
2. Multiply the fractions by 6:
(3x - 5) / 2 * 6 = (5x + 10) / 3
3. This gives you:
3(3x - 5) = 2(5x + 10)
4. Expand and simplify both sides:
9x - 15 = 10x + 20
5. Rearrange the equation by moving variables to one side and constants to the other:
9x - 10x = 20 + 15
6. Solve for x:
-x = 35
7. Finally, to express the solution as an improper fraction, we can rewrite -x as -35/1.
Therefore, the solution to the equation (3x - 5) / 2 = (5x + 10) / 3 is x = -35/1.
