The inequality you provided is:

$x + 3 < 6x - 4$

Let's solve this step by step:

1. Subtract $x$ from both sides to bring the variable terms together: $3 < 5x - 4$

2. Add 4 to both sides to isolate the variable term on the right: $3 + 4 < 5x$ $7 < 5x$

3. Divide both sides by 5 to solve for $x$: $\frac{7}{5} < x$

This can also be written as: $x > \frac{7}{5}$

So, the solution is:

$x > \frac{7}{5}$

Would you like further details or clarifications on any steps?

Here are some related questions for further practice:

1. How would you graph the solution $x > \frac{7}{5}$?
2. How does the inequality change if the coefficients of $x$ were negative?
3. What happens if you add $4$ to both sides of the original inequality?
4. Can this inequality have an equivalent absolute value form?
5. How do you check if a value satisfies the inequality?

Tip: When solving inequalities, if you multiply or divide both sides by a negative number, don't forget to flip the inequality sign!