Since the denominators are 3 and 4, the lcd will be 12.
Multiply the lcd on both sides.
By doing that we will have:
4*2(x-2) + 3*3 = 3*5(2x + 3)
8(x - 2) + 9 = 15(2x + 3)
Apply Distributive Property: a(b + c) = a*b + a *c.
8x - 16 + 9 = 30x + 45
8x - 7 = 30x + 45
Put the terms with x on one side, and the constants on the other side.
8x - 30x = 45 + 7
Combine like terms.
-22x = 52
Isolate the x on left side by multiply -1/22 on each side.
x = -52/22
The gcf is 11 so, divide the top and bottom by 11.
The final answer is -26/11.