To solve the equation 3/4x + 3 - 2x = -1/4 + 1/2x + 5, we first need to simplify both sides by combining like terms:
3/4x - 2x + 3 = -1/4 + 1/2x + 5
Next, we can simplify the fractions on the right side by finding a common denominator of 4:
3/4x - 2x + 3 = -1/4 + 2/4x + 20/4
Simplifying the right side further, we get:
3/4x - 2x + 3 = 19/4 + 1/2x
Now we can isolate the variable x by moving all the terms containing x to one side of the equation and all the constants to the other side:
3/4x - 2x - 1/2x = 19/4 - 3
Combining like terms:
-5/4x = 5/4
Finally, we can solve for x by multiplying both sides by the reciprocal of -5/4:
x = -1
Therefore, the solution to the equation is x = -1.