Question

Solve the inequality.

|d + 2| ≥ 6


d ≤ −8 or d ≥ −4


d ≤ −4 or d ≥ 4


d ≥ −8 or d ≥ 4


d ≤ −8 or d ≥ 4

Answer 1

To solve the inequality \(|d + 2| ≥ 6\), we need to consider the definition of absolute value. The expression \(|x| ≥ a\) results in two cases:

1. \(x ≥ a\)
2. \(x ≤ -a\)

Applying this to our inequality \(|d + 2| ≥ 6\), we can split it into two separate inequalities:

1. \(d + 2 ≥ 6\)
2. \(d + 2 ≤ -6\)

Now, we'll solve each inequality separately.

### For the first inequality:

\[
d + 2 ≥ 6
\]
Subtracting 2 from both sides:
\[
d ≥ 4
\]

### For the second inequality:

\[
d + 2 ≤ -6
\]
Subtracting 2 from both sides:
\[
d ≤ -8
\]

### Conclusion

Combining both results, we have:
\[
d ≤ -8 \quad \text{or} \quad d ≥ 4
\]

Thus, the solution to the inequality \(|d + 2| ≥ 6\) is:

\[
\boxed{d ≤ -8 \text{ or } d ≥ 4}
\]