Three times the sum of half Carlita’s age and 3 is at least 12. What values represent Carlita’s possible age?
Let's represent Carlita's age as "x".
Half of Carlita's age is (1/2)x.
The sum of half of Carlita's age and 3 is (1/2)x + 3.
Three times the sum of half of Carlita's age and 3 is 3[(1/2)x + 3] = (3/2)x + 9.
We are given that this expression is at least 12, so we can write the inequality:
(3/2)x + 9 ≥ 12.
Subtracting 9 from both sides, we have:
(3/2)x ≥ 3.
Multiplying both sides by 2/3, we have:
x ≥ 2.
Therefore, Carlita's age must be greater than or equal to 2. Since age cannot be negative, the possible values for Carlita's age are any value greater than or equal to 2.