Given an arithmetic series with common difference d=4, T4=3x−1, and T7=2x+8, determine the value of x and the first term of the series.

The common difference is $d = 4$.
The fourth term is $T_4 = 3x-1$.
The seventh term is $T_7 = 2x+8$.
The formula for the $n$-th term of an arithmetic series is $T_n = a + (n-1)d$.

The difference between the seventh term and the fourth term is $3d$.

Subtract $2x$ from both sides:

Subtract 11 from both sides:

The value of $x$ is $\boxed{-3}$.

2.1.2 Calculate the:

a) First term of the series

We know $T_4 = -10$, $n=4$, and $d=4$.

The first term of the series is $\boxed{-22}$.

b) Sum of the first 42 terms of the series

First term $a = -22$ (from 2.1.2a).
Common difference $d = 4$.
Number of terms $n = 42$.
The formula for the sum of the first $n$ terms of an arithmetic series is $S_n = \frac{n}{2}[2a + (n-1)d]$.

The sum of the first 42 terms of the series is $\boxed{2520}$.