To solve the equation 0.5x + (4/5)x = x + 9, we can start by simplifying the equation.
Combining like terms, we have (0.5 + 4/5)x = x + 9.
To get rid of the fractions, we can multiply both sides of the equation by the least common denominator of 5, which is 5.
This gives us (5/10 + 4/5)x = 5x/5 + 9(5).
Simplifying further, we have (1/2 + 4/5)x = x + 45.
To add the fractions, we need a common denominator. The least common denominator of 2 and 5 is 10.
So, we have (5/10 + 8/10)x = x + 45.
Combining the fractions, we get (13/10)x = x + 45.
To isolate the variable x, we can subtract x from both sides of the equation.
This gives us (13/10)x - x = 45.
Simplifying, we have (3/10)x = 45.
To solve for x, we can multiply both sides of the equation by the reciprocal of 3/10, which is 10/3.
This gives us x = (45)(10/3).
Simplifying further, x = 150/3.
Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.
This gives us x = 50.
So, the solution set to the equation 0.5x + (4/5)x = x + 9 is x = 50.