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.

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.