Question

Which of the following statements says that a number is between -3 and 3?



|x| = 3

|x| < 3

|x| > 3

Answer 1

the first one

Answer 2

\(\large { |x|=3\implies
\begin{cases}
+x=3\implies x=3\\
-x=3\implies x=-3
\end{cases}\implies x=\pm 3

\\ \quad \\

|x|<3\implies
\begin{cases}
+x<3\implies x<3\\
-x<3\implies x>-3
\end{cases}\implies -3<x<3
\\ \quad \\

|x|>3\implies
\begin{cases}
+x>3\implies x>3\\
-x>3\implies x<-3
\end{cases}\implies 3 < x < -3 } \)

recall that when multiplying an inequality by a negative value, you'd need to flip the inequality sign

any ideas?