Given `T_(3)` in the expansion of `(1-3x)^6` has maximum numerical value .Find the range of 'x '

Explanation

To solve the problem of finding the range of \( x \) for which the term \( T_3 \) in the expansion of \( (1 - 3x)^6 \) has the maximum numerical value, we can follow these steps:

### Step 1: Identify the general term in the binomial expansion
The general term \( T_k \) in the binomial expansion of \( (a + b)^n \) is given by:
\[ T_k = \binom{n}{k-1} a^{n-k+1} b^{k-1} \]
For our case, \( a = 1 \), \( b = -3x \), and \( n = 6 \). Therefore, the general term \( T_k \) is:
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