Solve 18-3x^2>0

$$18 - 3 x ^ { 2 } > 0$$

Solve for x

$$x\in \left(-\sqrt{6},\sqrt{6}\right)$$

Solution Steps

Multiply the inequality by -1 to make the coefficient of the highest power in 18-3x^{2} positive. Since -1 is negative, the inequality direction is changed.

$$-18+3x^{2}<0$$

Add 6 to both sides.

$$x^{2}<6$$

Calculate the square root of 6 and get \sqrt{6}. Rewrite 6 as \left(\sqrt{6}\right)^{2}.

$$x^{2}<\left(\sqrt{6}\right)^{2}$$

Inequality holds for |x|<\sqrt{6}.

$$|x|<\sqrt{6}$$

Rewrite |x|<\sqrt{6} as x\in \left(-\sqrt{6},\sqrt{6}\right).

$$x\in \left(-\sqrt{6},\sqrt{6}\right)$$