To solve the inequality $4x^2 < 25$ algebraically, let's proceed with the following steps:

1. Isolate $x^2$: $4x^2 < 25$ Divide both sides by 4: $x^2 < \frac{25}{4}$

2. Take the Square Root: To solve $x^2 < \frac{25}{4}$, take the square root of both sides, keeping in mind that this will produce both positive and negative solutions: $-\sqrt{\frac{25}{4}} < x < \sqrt{\frac{25}{4}}$ Simplify the square root: $-\frac{5}{2} < x < \frac{5}{2}$

Thus, the solution is: $-\frac{5}{2} < x < \frac{5}{2}$

Correct Answer: The correct answer choice is the fourth option: $-\frac{5}{2} < x < \frac{5}{2}$

Would you like further details, or do you have any questions?

Here are some related questions to deepen your understanding:

1. How do you handle inequalities with variables inside absolute values?
2. What changes if the inequality is $4x^2 \leq 25$ instead of $4x^2 < 25$?
3. How would you solve a similar inequality if the coefficient of $x^2$ was negative?
4. What if the inequality was $4x^2 > 25$? How would the solution change?
5. How do you handle inequalities involving fractions and negative coefficients?

Tip: Always remember to consider both positive and negative roots when dealing with squared terms in inequalities.