Final answer:
To solve the inequality 3|x+1|≥-6, consider cases when x+1 is positive and when x+1 is negative. Express the solution in interval notation as [-7/3, ∞) U [-5, ∞).
Step-by-step explanation:
To solve the inequality 3|x+1|≥-6, we need to consider two cases: when x+1 is positive and when x+1 is negative.
When x+1 is positive, the inequality becomes 3(x+1)≥-6. Solving for x gives x≥-7/3.
When x+1 is negative, the inequality becomes 3(-(x+1))≥-6. Solving for x gives x≥-5.
Since we have two separate conditions, we can express the solution in interval notation as [-7/3, ∞) U [-5, ∞).