Let's solve the inequality:

Given:

\[
4x + 1 < 4(x - 9)
\]

### Step-by-step solution:

1. **Distribute the 4 on the right-hand side:**
\[
4x + 1 < 4x - 36
\]

2. **Subtract \( 4x \) from both sides:**
\[
1 < -36
\]

This results in a contradiction, since \( 1 \) is not less than \( -36 \). Therefore, the inequality has **no solution**.

### Conclusion:
There is no value of \( x \) that satisfies the inequality.

Would you like any further details or have any questions?

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Here are 5 related questions to consider:

1. How would the solution change if it were an equality instead of an inequality?
2. What happens if the inequality symbol is reversed?
3. Can you graph this inequality on a number line?
4. What are some examples of inequalities that have a solution?
5. How would you solve \( 2x + 5 < 3(x - 4) \)?

**Tip:** Always check if an inequality leads to a contradiction before proceeding further.

Explore the solution to the inequality 4x + 1 < 4(x - 9) through a step-by-step process. Learn about algebraic concepts like distribution and properties of inequalities. Suitable for students in Grades 7-9.

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