(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is :

Given,

(x + 3), 1, (3x − 7) and −5 are in proportion.

$$\begin{aligned}\therefore \frac{(x + 3)}{1} = \frac{(3x - 7)}{-5} \\[1em] \Rightarrow (x + 3)= \frac{(3x - 7)}{-5} \\[1em] \Rightarrow -5(x + 3) = (3x - 7) \\[1em] \Rightarrow -5x - 15 = 3x - 7 \\[1em] \Rightarrow -5x - 3x = 15 - 7 \\[1em] \Rightarrow -8x = 8 \\[1em] \Rightarrow x = -\frac{8}{8} \\[1em] \Rightarrow x = -1.\end{aligned}$$

Hence, option 1 is the correct option.