Solve 4w^2-9geq0

$$4 { w }^{ 2 } -9 \geq 0$$

Solve for w

$$w\in (-\infty,-\frac{3}{2}]\cup [\frac{3}{2},\infty)$$

Solution Steps

Add \frac{9}{4} to both sides.

$$w^{2}\geq \frac{9}{4}$$

Calculate the square root of \frac{9}{4} and get \frac{3}{2}. Rewrite \frac{9}{4} as \left(\frac{3}{2}\right)^{2}.

$$w^{2}\geq \left(\frac{3}{2}\right)^{2}$$

Inequality holds for |w|\geq \frac{3}{2}.

$$|w|\geq \frac{3}{2}$$

Rewrite |w|\geq \frac{3}{2} as w\leq -\frac{3}{2}\text{; }w\geq \frac{3}{2}.

$$w\leq -\frac{3}{2}\text{; }w\geq \frac{3}{2}$$