Solve for x
x\in \left(-\frac{2\sqrt{3}}{3},\frac{2\sqrt{3}}{3}\right)
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\frac{3}{4}x^{2}-1<0
Multiply the inequality by -1 to make the coefficient of the highest power in -\frac{3}{4}x^{2}+1 positive. Since -1 is negative, the inequality direction is changed.
x^{2}<\frac{4}{3}
Add \frac{4}{3} to both sides.
x^{2}<\left(\frac{2\sqrt{3}}{3}\right)^{2}
Calculate the square root of \frac{4}{3} and get \frac{2\sqrt{3}}{3}. Rewrite \frac{4}{3} as \left(\frac{2\sqrt{3}}{3}\right)^{2}.
|x|<\frac{2\sqrt{3}}{3}
Inequality holds for |x|<\frac{2\sqrt{3}}{3}.
x\in \left(-\frac{2\sqrt{3}}{3},\frac{2\sqrt{3}}{3}\right)
Rewrite |x|<\frac{2\sqrt{3}}{3} as x\in \left(-\frac{2\sqrt{3}}{3},\frac{2\sqrt{3}}{3}\right).
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