Solve 2m^2>4

$$2 m ^ { 2 } > 4$$

Solve for m

$$m\in \left(-\infty,-\sqrt{2}\right)\cup \left(\sqrt{2},\infty\right)$$

Solution Steps

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$m^{2}>\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$m^{2}>2$$

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

$$m^{2}>\left(\sqrt{2}\right)^{2}$$

Inequality holds for |m|>\sqrt{2}.

$$|m|>\sqrt{2}$$

Rewrite |m|>\sqrt{2} as m<-\sqrt{2}\text{; }m>\sqrt{2}.

$$m<-\sqrt{2}\text{; }m>\sqrt{2}$$