The given inequality is $|5 - 4x| > 8$. Let's solve this step-by-step:

Step 1: Break the absolute value inequality

For an inequality of the form $|A| > B$, where $B > 0$, the solution is split into two cases:

1. $A > B$
2. $A < -B$

So, we break the inequality $|5 - 4x| > 8$ into two cases:

• $5 - 4x > 8$
• $5 - 4x < -8$

Step 2: Solve each inequality

Case 1: $5 - 4x > 8$

Subtract 5 from both sides: $-4x > 3$ Divide by $-4$ (and reverse the inequality sign): $x < -\frac{3}{4}$

Case 2: $5 - 4x < -8$

Subtract 5 from both sides: $-4x < -13$ Divide by $-4$ (and reverse the inequality sign): $x > \frac{13}{4}$

Step 3: Combine the solutions

The combined solution from both cases is: $x < -\frac{3}{4} \quad \text{or} \quad x > \frac{13}{4}$

In interval notation, this is: $(-\infty, -\frac{3}{4}) \cup (\frac{13}{4}, \infty)$

Step 4: Match with the options

From the provided options in the image, the correct one is: $(-\infty, -\frac{3}{4}) \cup (\frac{13}{4}, \infty)$

This corresponds to the second option in the list.

Would you like more details on any part of the solution? Here are five related questions to practice:

1. How do you solve absolute value inequalities of the form $|A| < B$?
2. What happens if $B = 0$ in an absolute value inequality $|A| > B$?
3. Can you graph the solution of $|5 - 4x| > 8$ on a number line?
4. How do you solve compound inequalities involving "and" or "or"?
5. What is the general rule for reversing inequality signs when multiplying or dividing by a negative number?

Tip: Always remember to reverse the inequality sign when dividing or multiplying both sides of an inequality by a negative number.