Solve 2x^2geq2

$$2 x ^ { 2 } \geq 2$$

Solve for x

$$x\in (-\infty,-1]\cup [1,\infty)$$

Solution Steps

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

$$x^{2}\geq \frac{2}{2}$$

Divide 2 by 2 to get 1.

$$x^{2}\geq 1$$

Calculate the square root of 1 and get 1. Rewrite 1 as 1^{2}.

$$x^{2}\geq 1^{2}$$

Inequality holds for |x|\geq 1.

$$|x|\geq 1$$

Rewrite |x|\geq 1 as x\leq -1\text{; }x\geq 1.

$$x\leq -1\text{; }x\geq 1$$