We are tasked with solving the inequality:

\[
-3x + 17 < -13
\]

### Step-by-Step Solution:

1. **Subtract 17 from both sides** to begin isolating \( x \):

\[
-3x + 17 - 17 < -13 - 17
\]

This simplifies to:

\[
-3x < -30
\]

2. **Divide both sides by -3**. Since we are dividing by a negative number, we must **reverse the inequality sign**:

\[
x > \frac{-30}{-3}
\]

This simplifies to:

\[
x > 10
\]

### Final Answer:
\[
x > 10
\]

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Would you like further details or have any questions about the steps?

Here are 5 related questions for practice:
1. Solve \( 4x - 7 \leq 9 \).
2. Solve \( 2x + 5 > 3x - 2 \).
3. Solve \( -5x + 3 \geq 8 \).
4. Solve \( \frac{3x + 1}{2} < 5 \).
5. Solve \( -2x - 4 \leq 6 \).

**Tip:** Remember, when multiplying or dividing both sides of an inequality by a negative number, always reverse the direction of the inequality sign.

Learn how to solve the linear inequality -3x + 17 < -13 with a detailed, step-by-step breakdown. This example demonstrates key algebraic concepts like inequality reversal when dividing by a negative number. Ideal for students in Grades 7-9.

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