We can solve the inequality step-by-step:

\[
-7 + 7x \leq -14
\]

### Step 1: Add 7 to both sides to isolate the term with \(x\).
\[
7x \leq -14 + 7
\]
\[
7x \leq -7
\]

### Step 2: Divide both sides by 7 to solve for \(x\).
\[
x \leq \frac{-7}{7}
\]
\[
x \leq -1
\]

### Final Answer:
\[
x \leq -1
\]

Let me know if you want further details or clarifications!

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Here are some related questions to explore:

1. How would the solution change if it was \( -7 + 7x = -14 \)?
2. What is the solution for \( -7 + 7x > -14 \)?
3. How would the solution change if the inequality was \( -7 + 7x \geq -14 \)?
4. Can you explain how dividing by a negative number affects inequalities?
5. What happens if you graph the inequality \( x \leq -1 \)?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the linear inequality -7 + 7x <= -14 with a detailed step-by-step solution. This problem involves fundamental algebraic concepts and inequality rules. Suitable for students in Grades 7-9.

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