To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we can break it into two parts:
1. \(-2 \leq 2x + 13 - 4\)
2. \(2x + 13 - 4 < 1\)
First, simplify the expression:
\[
2x + 13 - 4 = 2x + 9
\]
Now we have the compound inequality:
\[
-2 \leq 2x + 9 < 1
\]
Now, let's solve both parts.
### Solve the left part:
\[
-2 \leq 2x + 9
\]
Subtract 9 from both sides:
\[
-2 - 9 \leq 2x \implies -11 \leq 2x
\]
Divide by 2:
\[
-\frac{11}{2} \leq x \implies x \geq -\frac{11}{2}
\]
### Solve the right part:
\[
2x + 9 < 1
\]
Subtract 9 from both sides:
\[
2x < 1 - 9 \implies 2x < -8
\]
Divide by 2:
\[
x < -4
\]
### Combine the results:
So now we have:
\[
-\frac{11}{2} \leq x < -4
\]
### Convert \(-\frac{11}{2}\) to decimal:
\(-\frac{11}{2} = -5.5\).
Thus, the solution can be written in interval notation as:
\[
[-\frac{11}{2}, -4)
\]
Now let's check the given options. You specifically asked for an option that matches:
- \(\{x: -\frac{11}{2} \leq x < -4\}\)
### Which response matches?
None of the given responses match our derived solution.
The correct answer would be the set:
\(\{x: -\frac{11}{2} \leq x < -4 \}\).
If you meant to have an option that I didn't see or if there was any confusion, please clarify, and I can help you further!