Final answer:
To simplify the expression 0.5 + 3(z + 12) + 5(z + 3), distribute and combine like terms to get 8z + 51.5.
Step-by-step explanation:
To simplify the expression 0.5 + 3(z + 12) + 5(z + 3), we need to apply the distributive property and combine like terms. Applying the distributive property to the terms with parentheses gives us:
- 3(z + 12) = 3z + 36
- 5(z + 3) = 5z + 15
Putting it all together, we have 0.5 + 3z + 36 + 5z + 15. We can combine the like terms to simplify further:
- Combine the z terms: 3z + 5z = 8z
- Combine the constant terms: 0.5 + 36 + 15 = 51.5
So the simplified expression is 8z + 51.5.