To solve the equation, we need to first convert the mixed numbers to improper fractions:

1 1/2 = 3/2
3 3/4 = 15/4

Now we have: (3/2 + 15/4) × x = 4.5

Find a common denominator:

(3/2 + 15/4) = (6/4 + 15/4) = 21/4

Replace the sum in the equation:

(21/4) × x = 4.5

Now solve for x:

(21/4) × x = 4.5
21x/4 = 4.5
21x = 4.5 * 4
21x = 18
x = 18/21
x = 6/7

Therefore, the solution to the equation is x = 6/7.