Final answer:
The compound inequality -4 > 8 - 4q > -12 is true if the value of q is between 3 and 5. By solving the inequality step-by-step, we find that the statement holds for values within this range. Hence, the inequality is true for 3 < q < 5.
Step-by-step explanation:
The inequality -4 > 8 - 4q > -12 is a compound inequality. To check if the statement is true or false, we need to break it down into two parts: -4 > 8 - 4q and 8 - 4q > -12. Solving the first part, we subtract 8 from both sides to get -12 > -4q, or q > 3 when we divide by -4 and flip the inequality sign due to division by a negative number. For the second part, we subtract 8 from both sides to get -4q > -20, which simplifies to q < 5 after dividing by -4. However, since the compound inequality states that q must be greater than 3 but also less than 5, this leaves us with the solution 3 < q < 5.
Solving the question using rules of inequalities, the compound inequality is true for values of q that are between 3 and 5 (3 < q < 5). If we assume a value within the range, for example, q = 4, the compound inequality holds true (-4 > 8 - 4(4) > -12 simplifies to -4 > 8 - 16 > -12, which becomes -4 > -8 > -12, verifying the inequality).