Solve 4x^2-1geq0

$$4 x ^ { 2 } - 1 \geq 0$$

Solve for x

$$x\in (-\infty,-\frac{1}{2}]\cup [\frac{1}{2},\infty)$$

Solution Steps

Add \frac{1}{4} to both sides.

$$x^{2}\geq \frac{1}{4}$$

Calculate the square root of \frac{1}{4} and get \frac{1}{2}. Rewrite \frac{1}{4} as \left(\frac{1}{2}\right)^{2}.

$$x^{2}\geq \left(\frac{1}{2}\right)^{2}$$

Inequality holds for |x|\geq \frac{1}{2}.

$$|x|\geq \frac{1}{2}$$

Rewrite |x|\geq \frac{1}{2} as x\leq -\frac{1}{2}\text{; }x\geq \frac{1}{2}.

$$x\leq -\frac{1}{2}\text{; }x\geq \frac{1}{2}$$