Question

If \( x^2 + 2x + 7<6 \), \( x \in \mathbb{R} \), then:

• A. \( x>11 \) or \( x<-3/2 \)
• B. \( x>11 \) or \( x<-1 \)
• C. \( -3/2<x<-1 \)
• D. \( -1<x<11 \)

Hint:

To solve quadratic inequalities, first solve the equality and then analyze the sign of the quadratic expression.

Answer 1

The Correct Option is D

Step 1: Solve the inequality.
Solving the quadratic inequality \( x^2 + 2x + 7<6 \), we find that the solution is \( -1<x<11 \).
Step 2: Conclusion.
Thus, the correct answer is \( -1<x<11 \).
Final Answer: \[ \boxed{-1<x<11} \]