Answer
$ 260 \le T(c) \le 538 $
Work Step by Step
We know the formula: $T(F) = (1.8 \times T(c)) +32$
We have the inequality:
$ 500 \lt T(F) \lt 1000$
We substitute:
$ 500 \lt T(F) = (1.8 \times T(c)) +32 \lt 1000$
Now, follow PEMDAS. In other words, first address parentheses, and then resolve exponents. Next, simplify division and multiplication, and lastly address subtraction and addition. This gives:
$ 260 \le T(c) \le 538 $