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To solve the inequality \( 13 - 4x > 37 \), let’s proceed step-by-step:

### Step 1: Isolate the term with \( x \).
Subtract 13 from both sides of the inequality:
\[
-4x > 37 - 13
\]
\[
-4x > 24
\]

### Step 2: Solve for \( x \).
Now, divide both sides by -4. **Remember** that dividing by a negative number reverses the inequality sign:
\[
x < \frac{24}{-4}
\]
\[
x < -6
\]

### Final Answer:
\[
x < -6
\]

Let me know if you'd like more details or if you have any questions.

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Here are five related questions that build on this problem:
1. How would the solution change if the inequality were \( 13 - 4x \geq 37 \)?
2. Can you explain why dividing by a negative number reverses the inequality sign?
3. What if the inequality was \( 13 + 4x > 37 \)? How would you solve it?
4. How can we check if a particular value of \( x \) satisfies the inequality \( 13 - 4x > 37 \)?
5. If we graph the inequality \( x < -6 \) on a number line, what would it look like?

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

Solve the inequality for x: 13 - 4x > 37. Simplify your answer as much as possible.

Learn how to solve the inequality 13 - 4x > 37 with a detailed, step-by-step solution. This problem demonstrates key algebra concepts, including the properties of inequalities and reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 8-10.

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