To solve the equation, let's simplify and combine like terms:
x + 2 1/2 = 4x + 3/4 - 2 - 3x/8
First, let's convert the mixed numbers to improper fractions:
x + 5/2 = 4x + 3/4 - 8/4 - 3x/8
Next, let's combine the fractions:
x + 5/2 = 4x - 5/4 - 3x/8
To eliminate the denominators, let's multiply each term by 8:
8(x + 5/2) = 8(4x - 5/4 - 3x/8)
Simplifying further:
8x + 20 = 32x - 10 - 3x
Combine like terms:
8x + 20 = 29x - 10
Move the variables to one side and constants to the other side:
8x - 29x = -10 - 20
-21x = -30
Divide both sides by -21:
x = -30/-21
Simplifying the fraction:
x = 10/7
Therefore, the solution to the equation is x = 10/7.