Final answer:
To make the equation –(8+4) ÷ [] = -6 true, the correct value to fill in the blank is 2, as –(12) ÷ (-6) = 2. The solution is found by following the rules of addition and division for negative and positive numbers. Option C is the correct answer.
Step-by-step explanation:
The student is asking to fill in the blank to make the mathematical equation –(8+4)÷[] = -6 true. To solve this, consider the equation step by step. First, calculate the sum within the parentheses, which is –(8+4) = –(12). Next, to solve for the blank, let's represent the blank with the variable x. The equation now is –(12) ÷ x = -6.
To find x, divide -12 by -6. The rules for division indicate that dividing two numbers with similar signs results in a positive outcome. Therefore, –(12) ÷ (-6) = 2. So, the value that makes the equation true is 2, which corresponds to option C.