Question

If x^2+3<4 and 2x^2+3>4, what is a possible value of x?

Answer 1

x^2+3<4 and 2x^2+3>4
\[
x^2 < 1\\
-1< x < 1\\
2x^2+3>4\\
2 x^2 > 1\\
x^2> 1/2\\
x< -\frac{\sqrt 2}2 ,\quad x>\frac{\sqrt 2}2
\]

What's for both?

Answer 2

x<-1 and x<1

Answer 3

\[
-1< x < -\frac {\sqrt 2}2 \quad \text{ or } \quad \frac {\sqrt 2}2 < x < 1
\]

Answer 4

so it can be -1 or 1, right?

Answer 5

No if you have strict inequality to begin with.

Answer 6

i dont think we do here

Answer 7

So the answer is
\[
-1< x < -\frac {\sqrt 2}2 \quad \text{ or } \quad \frac {\sqrt 2}2 < x < 1
\]