Question

Solve the compound inequality.
-6 /leq 9 + 3y /leq 6

Answer 1

To solve the compound inequality \(-6 \leq 9 + 3y \leq 6\), we can break it into two parts and solve them separately.

1. **Solve the left part:**
\[
-6 \leq 9 + 3y
\]
Subtract 9 from both sides:
\[
-6 - 9 \leq 3y
\]
\[
-15 \leq 3y
\]
Now, divide by 3:
\[
-5 \leq y
\]

2. **Solve the right part:**
\[
9 + 3y \leq 6
\]
Subtract 9 from both sides:
\[
3y \leq 6 - 9
\]
\[
3y \leq -3
\]
Now, divide by 3:
\[
y \leq -1
\]

Combining both parts, we have:
\[
-5 \leq y \leq -1
\]

Thus, the solution to the compound inequality is:
\[
\boxed{[-5, -1]}
\]