Question

What is the solution to the inequality below? x2 < 25 O A. x>5 and x < -5 B. X> 5 orx < -5 O C. x < 5 and x>-5 O D. x< 5 or x>-5

Answer 1

`\begin{gathered} \text{Given} \\ x^2<25 \end{gathered}`

First find the critical points by equating the two terms

`\begin{gathered} x^2=25 \\ \sqrt[]{x^2}=\sqrt[]{25} \\ x=\pm5 \end{gathered}`

Then test out the intervals between critical points.

`\begin{gathered} \text{If }x>5,\text{ we will use }x=6 \\ 6^2<25 \\ 36<25 \\ x>5\text{ does not work} \\ \\ \text{If }x>-5,\text{ we will use }x=3 \\ 3^2<25 \\ 9<25 \\ x>-5\text{ works} \\ \\ \text{If }x<5,\text{ we will use }x=4 \\ 4^2<25 \\ 16<25 \\ x<5\text{ works} \end{gathered}`

Therefore the solution is x < 5, and x > -5.