To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we first simplify the expression in the middle:
\[ -2 \leq 2x + 9 < 1 \]
Now, we can break this into two separate inequalities to solve:
- \(-2 \leq 2x + 9\)
- \(2x + 9 < 1\)
Solving the first inequality:
\(-2 \leq 2x + 9\)
Subtract 9 from both sides:
\[ -2 - 9 \leq 2x \ -11 \leq 2x \]
Now, divide both sides by 2:
\[ -\frac{11}{2} \leq x \quad \text{or} \quad x \geq -5.5 \]
Solving the second inequality:
\(2x + 9 < 1\)
Subtract 9 from both sides:
\[ 2x < 1 - 9 \ 2x < -8 \]
Now, divide both sides by 2:
\[ x < -4 \]
Combining both solutions:
So, we have the two inequalities combined:
\[ -\frac{11}{2} \leq x < -4 \]
In decimal form, this is:
\[ -5.5 \leq x < -4 \]
From the provided responses, none of them match this solution exactly. However, it appears that based on numerical ranges and choices given, it seems like there might be a misunderstanding in matching inequalities. Please double-check the values provided in your options against the computed ranges. If the provided responses remain as listed, they do not represent the solution to the compound inequality you provided.