State the values of $|x|$ for which the binomial expansion of $(3 + 2x)^{4}$ is valid - AQA - A-Level Maths Mechanics - Question 1 - 2017 - Paper 2

The binomial expansion of $(a + b)^{n}$ is valid when the absolute value of the ratio of $b$ to $a$ is less than 1. In this case, $a = 3$ and $b = 2x$. Therefore, we need:

$|2x| < 3$

This can be simplified to:

$|x| < \frac{3}{2}$

Thus, the correct answer is: $|x| < \frac{3}{2}$.