Solve -4x^2>-8

$$-4 { x }^{ 2 } > -8$$

Solve for x

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

Solution Steps

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x^{2}<\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$x^{2}<2$$

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

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

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

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

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

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