We are given the inequality:

$6x - 1 < 2x - 6$

Step 1: Move all terms involving $x$ to one side

Subtract $2x$ from both sides of the inequality:

$6x - 2x - 1 < -6$

This simplifies to:

$4x - 1 < -6$

Step 2: Isolate the $x$-term

Now, add 1 to both sides of the inequality:

$4x < -6 + 1$

This simplifies to:

$4x < -5$

Step 3: Solve for $x$

Now, divide both sides by 4:

$x < \frac{-5}{4}$

Final Answer:

The solution is:

$x < -\frac{5}{4}$

In set notation, the solution can be written as:

$x \leq -\frac{5}{4}$

Let me know if you'd like any further details!

Here are some related questions you might find helpful:

1. What is the solution to $5x + 3 \geq 2x - 4$?
2. How do you solve the inequality $7x - 8 > 3x + 5$?
3. Can inequalities be solved the same way as equations?
4. How do you graph the solution to $x \leq -\frac{5}{4}$ on a number line?
5. What happens if you multiply or divide both sides of an inequality by a negative number?

Tip: Remember, when solving inequalities, if you multiply or divide by a negative number, you must reverse the inequality sign!