To solve the compound inequality [tex]\(-11 < 2x + 5 < 17\)[/tex], we will break it into two separate inequalities and solve each one step-by-step.
### Step 1: Solve the left side of the inequality [tex]\(-11 < 2x + 5\)[/tex]
1. Subtract 5 from both sides:
[tex]\[
-11 - 5 < 2x + 5 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
-16 < 2x
\][/tex]
2. Divide both sides by 2:
[tex]\[
\frac{-16}{2} < \frac{2x}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
-8 < x
\][/tex]
### Step 2: Solve the right side of the inequality [tex]\(2x + 5 < 17\)[/tex]
1. Subtract 5 from both sides:
[tex]\[
2x + 5 - 5 < 17 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
2x < 12
\][/tex]
2. Divide both sides by 2:
[tex]\[
\frac{2x}{2} < \frac{12}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x < 6
\][/tex]
### Combining both results:
From the steps above, we have:
[tex]\[
-8 < x \quad \text{and} \quad x < 6
\][/tex]
Combining the two inequalities, we obtain:
[tex]\[
-8 < x < 6
\][/tex]
Thus, the solution to the compound inequality [tex]\(-11 < 2x + 5 < 17\)[/tex] is:
[tex]\[
\boxed{-8 < x < 6}
\][/tex]
Hence, the correct option is:
d. [tex]\(-8 < x < 6\)[/tex]
