Let's solve the inequality:

\[
6x - 5(2x + 9) < 2x + 3
\]

### Steps:

1. **Distribute** the \( -5 \) on the left-hand side:
\[
6x - 10x - 45 < 2x + 3
\]

2. **Combine like terms** on the left-hand side:
\[
-4x - 45 < 2x + 3
\]

3. **Move the \( x \)-terms** to one side by adding \( 4x \) to both sides:
\[
-45 < 6x + 3
\]

4. **Move the constant term** \( 3 \) to the left-hand side by subtracting 3 from both sides:
\[
-45 - 3 < 6x
\]
\[
-48 < 6x
\]

5. **Solve for \( x \)** by dividing both sides by 6:
\[
\frac{-48}{6} < x
\]
\[
-8 < x
\]

Thus, the solution is \( x > -8 \).

Would you like any further details or additional clarification?

### Follow-up Questions:
1. How can you check if \( x > -8 \) is the correct solution?
2. How would the solution change if the inequality were \( \leq \) instead of \( < \)?
3. What happens if both sides of the inequality involve fractions?
4. How do you approach solving inequalities with exponents?
5. Can this inequality be graphed on a number line?
6. How do you handle inequalities that include absolute values?
7. What if the inequality involved more complex distribution?
8. Can inequalities like this be solved using substitution?

#### Tip: Be cautious when distributing negative signs, as they affect all the terms inside the parentheses. Always combine like terms before moving variables and constants to one side.

Learn how to solve the linear inequality 6x - 5(2x + 9) < 2x + 3 with detailed step-by-step solutions. This problem covers key algebraic concepts such as inequalities, distribution, combining like terms, and solving linear inequalities. Suitable for students in Grades 7-9.

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