Final Answer:
The solution to the inequality 3 * |x + 5| ≤ 6 is -5 ≤ x ≤ -3 (option c).
Step-by-step explanation:
To find the solution to the inequality, 3 * |x + 5| ≤ 6, we first isolate the absolute value expression. Dividing both sides by 3, we obtain |x + 5| ≤ 2. This implies that x + 5 lies between -2 and 2, leading to -2 ≤ x + 5 ≤ 2. Subtracting 5 from each part of the inequality yields -7 ≤ x ≤ -3. However, recognizing that |x + 5| cannot be negative, we refine the solution to -5 ≤ x ≤ -3.
In conclusion, the correct solution is -5 ≤ x ≤ -3 (option c). This interval ensures that the absolute value expression 3 * |x + 5| is less than or equal to 6, satisfying the given inequality.
Therefore, by systematically isolating the absolute value expression and considering the valid range for x + 5, we accurately determine that -5 ≤ x ≤ -3 is the solution to 3 * |x + 5| ≤ 6.