Question

Solve compound inequality.
x/2 >−1 and x+7<17
Answer should be a compound inequality

Answer 1

To solve the compound inequality \( \frac{x}{2} > -1 \) and \( x + 7 < 17 \), we will solve each part separately.

1. **Solve \( \frac{x}{2} > -1 \)**:
\[
\frac{x}{2} > -1
\]
Multiply both sides by 2 (since 2 is positive, the inequality direction remains the same):
\[
x > -2
\]

2. **Solve \( x + 7 < 17 \)**:
\[
x + 7 < 17
\]
Subtract 7 from both sides:
\[
x < 10
\]

Now we combine both results into a compound inequality:
\[
-2 < x < 10
\]

Thus, the solution to the compound inequality is:
\[
\boxed{-2 < x < 10}
\]