Algebra-1

To solve the inequality 3 |d + 1| - 7 ≥ -1, we can begin by adding 7 to both sides:

3 |d + 1| ≥ 6

Next, we can divide both sides by 3. However, we need to consider two cases based on the sign of (d + 1):

Case 1: d + 1 is nonnegative (i.e., d + 1 ≥ 0)
In this case, the absolute value |d + 1| is equal to d + 1, so we have:
3(d + 1) ≥ 6

Solving this inequality, we get:
3d + 3 ≥ 6
3d ≥ 6 - 3
3d ≥ 3
d ≥ 1

Case 2: d + 1 is negative (i.e., d + 1 < 0)
In this case, the absolute value |d + 1| is e...