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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!

Learn how to solve the inequality x + 3 < 6x - 4 step-by-step. This problem involves algebraic manipulation and inequality properties, making it suitable for students in Grades 6-8.

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