Let's solve the inequality:

\[
-5 - (14x - 1) < 2(7x - 16)
\]

### Steps:

1. **Distribute** the negative sign on the left-hand side and the \( 2 \) on the right-hand side:
\[
-5 - 14x + 1 < 14x - 32
\]

2. **Combine like terms** on the left-hand side:
\[
-14x - 4 < 14x - 32
\]

3. **Move the \( x \)-terms** to one side by adding \( 14x \) to both sides:
\[
-4 < 14x + 14x - 32
\]
\[
-4 < 28x - 32
\]

4. **Move the constant term** \( -32 \) to the left-hand side by adding 32 to both sides:
\[
28 < 28x
\]

5. **Solve for \( x \)** by dividing both sides by 28:
\[
\frac{28}{28} < x
\]
\[
1 < x
\]

Thus, the solution is \( x > 1 \).

Would you like any further details or additional clarification?

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

#### Tip: When working with inequalities, always be cautious about the direction of the inequality, especially when multiplying or dividing by negative numbers, as it reverses the inequality sign.

Learn how to solve the inequality -5 - (14x - 1) < 2(7x - 16) step-by-step with detailed explanations. This problem involves solving linear inequalities and manipulating terms to find the solution range for x. Suitable for students in Grades 9-12 studying algebra and inequalities.

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