Final answer:
The answer to whether the inequality -32c + 12 < -66 - 16 is true or false depends on the value of c. It is true if c <= 2.9375 and false if c > 2.9375. Without the value of c, we cannot determine a definitive answer.
Step-by-step explanation:
To determine if the inequality -32c + 12 < -66 - 16 is true or false, we must first simplify both sides of the inequality by performing the arithmetic operations. On the right-hand side, when we combine -66 and -16, the sum is -82. Therefore, our simplified inequality is:
-32c + 12 < -82
Next, we need to isolate the variable c on one side to see the value at which the inequality holds. To do this, we subtract 12 from both sides:
-32c + 12 - 12 < -82 - 12
-32c < -94
The next step is to divide both sides by -32 to solve for c. Remember, when dividing by a negative number, the inequality sign flips:
c > 2.9375
Therefore, without a specific value for c, we cannot categorically state whether the initial inequality is true or false; it depends on the value of c. If c is greater than 2.9375, then the inequality would be false. Otherwise, if c is less than or equal to 2.9375, the inequality would be true.
The answer depends on the value of c, and since the value is not given, the correct answer would be None of the above.