Answer :
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]
### 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]