Final answer:
To solve the inequality 3|w+3| ≤ 3, two conditions were analyzed based on the non-negativity of (w+3), yielding the solution -6 ≤ w ≤ 0, which in decimal form is -6.0 ≤ w ≤ 0.0.
Step-by-step explanation:
The question you've asked pertains to solving an inequality involving absolute values. The inequality 3|w+3| ≤ 3 can be solved by considering the definition of absolute value, which states that the value inside the absolute value signs can be either positive or negative and still satisfy the equation. We can set up two conditions: one where w+3 is non-negative, and one where w+3 is negative. Let's explore both conditions:
- If w+3 is non-negative (w+3 ≥ 0), we can remove the absolute value signs and write 3(w+3) ≤ 3. This simplifies to w ≤ 0.
- If w+3 is negative (w+3 < 0), we must consider the absolute value as the negation of w+3, leading to the inequality 3(-(w+3)) ≤ 3, which simplifies to w ≥ -6.
Combining both results, we find the solution to the inequality: -6 ≤ w ≤ 0. This interval is the range of values for w that satisfies the original inequality, and can be expressed in decimal form as -6.0 ≤ w ≤ 0.0.