Final answer:
To solve for x in the equation (2x-5)/(2)-(3x+9)/(10)=-2, rearrange the equation and solve by multiplying through by 10, expanding and collecting like terms, and then adding and dividing to find x = 2.
Step-by-step explanation:
To solve for x in the equation (2x-5)/(2)-(3x+9)/(10)=-2, we need to rearrange the equation and solve for x.
Multiplying through by 10 eliminates the denominators and gives us 10[(2x-5)/2] - [(3x+9)/10] = -20.
This simplifies to 5(2x-5) - (3x+9) = -20. Expanding and collecting like terms, we have 10x - 25 - 3x - 9 = -20.
Combining like terms, we get 7x - 34 = -20. Adding 34 to both sides and then dividing both sides by 7, we find that x = 2.