Question

Solve compound inequality.
x2 >−1 and x+7<17
Answer should be a compound inequality

Answer 1

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

1. **Solve \( x^2 > -1 \)**:
- The inequality \( x^2 > -1 \) is always true for all real numbers \( x \), because the square of a real number is always non-negative (greater than or equal to 0), and thus always greater than -1. So, we can say:
\[
\text{This part does not restrict } x.
\]

2. **Solve \( x + 7 < 17 \)**:
- To solve this inequality, we can isolate \( x \):
\[
x + 7 < 17 \\
x < 17 - 7 \\
x < 10
\]

Combining both parts, since the first part provides no restrictions, the final compound inequality based on the results obtained is:
\[
x < 10
\]

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