We need to solve the inequality $x - 9 < 3x + 1$ for $x$.

1. Problem Description

We need to solve the inequality $x - 9 < 3x + 1$ for $x$.

2. Solution Steps

We want to isolate $x$ on one side of the inequality.

First, subtract $x$ from both sides:

$x - 9 - x < 3x + 1 - x$

$-9 < 2x + 1$

Next, subtract 1 from both sides:

$-9 - 1 < 2x + 1 - 1$

$-10 < 2x$

Finally, divide both sides by 2:

$\frac{-10}{2} < \frac{2x}{2}$

$-5 < x$

This can also be written as:

$x > -5$

3. Final Answer

$x > -5$