To solve this inequality, we will first simplify it:
Starting with:[tex] {2x}^{2} < 3[/tex]
We can rewrite it as:[tex] 4x^2 < 3[/tex]
Dividing both sides by 4:[tex] x^2 < \frac{3}{4}[/tex]
Taking the square root of both sides:[tex] x < \sqrt{\frac{3}{4}}[/tex]
Simplifying the square root gives us:[tex] x < \frac{\sqrt{3}}{2}[/tex]
Therefore, the solution to the inequality is:[tex] x \in \left(-\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right)[/tex]
To solve this inequality, we will first simplify it:
Starting with:
[tex] {2x}^{2} < 3[/tex]
We can rewrite it as:
[tex] 4x^2 < 3[/tex]
Dividing both sides by 4:
[tex] x^2 < \frac{3}{4}[/tex]
Taking the square root of both sides:
[tex] x < \sqrt{\frac{3}{4}}[/tex]
Simplifying the square root gives us:
[tex] x < \frac{\sqrt{3}}{2}[/tex]
Therefore, the solution to the inequality is:
[tex] x \in \left(-\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right)[/tex]