[tex] {2x}^{2} < 3[/tex]

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вопрос

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]