Final answer:
The largest possible integer value of x for the expression (12-x)÷(3x) to represent a non-negative integer is 12.
Step-by-step explanation:
To find the largest possible integer value of x for the expression (12-x)÷(3x) to represent a non-negative integer, we need to determine the range of values for x. We can start by setting up the inequality (12-x)÷(3x) ≥ 0.
Simplifying further, we have (12-x) ≥ 0 and (3x) > 0. In order for a fraction to be positive, both the numerator and denominator must have the same sign.
Since (3x) > 0, we know that x > 0. To satisfy (12-x) ≥ 0, we find that x ≤ 12. Therefore, the largest possible integer value of x is 12.