How to solve 9(x)^(2) < 25

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 9(x)^(2) < 25 | Equatix

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$$9 { x }^{ 2 } < 25$$

$x\in \left(-\frac{5}{3},\frac{5}{3}\right)$

Divide both sides by $9$. Since $9$ is positive, the inequality direction remains the same.

$$x^{2}<\frac{25}{9}$$

Calculate the square root of $\frac{25}{9}$ and get $\frac{5}{3}$. Rewrite $\frac{25}{9}$ as $\left(\frac{5}{3}\right)^{2}$.

$$x^{2}<\left(\frac{5}{3}\right)^{2}$$

Inequality holds for $|x|<\frac{5}{3}$.

$$|x|<\frac{5}{3}$$

Rewrite $|x|<\frac{5}{3}$ as $x\in \left(-\frac{5}{3},\frac{5}{3}\right)$.

$$x\in \left(-\frac{5}{3},\frac{5}{3}\right)$$