Solve 13-4x^2>0

$$13 - 4 x ^ { 2 } > 0$$

Solve for x

$$x\in \left(-\frac{\sqrt{13}}{2},\frac{\sqrt{13}}{2}\right)$$

Solution Steps

Multiply the inequality by -1 to make the coefficient of the highest power in 13-4x^{2} positive. Since -1 is negative, the inequality direction is changed.

$$-13+4x^{2}<0$$

Add \frac{13}{4} to both sides.

$$x^{2}<\frac{13}{4}$$

Calculate the square root of \frac{13}{4} and get \frac{\sqrt{13}}{2}. Rewrite \frac{13}{4} as \left(\frac{\sqrt{13}}{2}\right)^{2}.

$$x^{2}<\left(\frac{\sqrt{13}}{2}\right)^{2}$$

Inequality holds for |x|<\frac{\sqrt{13}}{2}.

$$|x|<\frac{\sqrt{13}}{2}$$

Rewrite |x|<\frac{\sqrt{13}}{2} as x\in \left(-\frac{\sqrt{13}}{2},\frac{\sqrt{13}}{2}\right).

$$x\in \left(-\frac{\sqrt{13}}{2},\frac{\sqrt{13}}{2}\right)$$