To solve the inequality:

$5|5 - x| + 4 < 44$

Step 1: Isolate the absolute value term. First, subtract 4 from both sides:

$5|5 - x| < 40$

Step 2: Divide by 5. Divide both sides of the inequality by 5 to simplify:

$|5 - x| < 8$

Step 3: Solve the absolute value inequality. The general rule for solving an inequality of the form $|A| < B$ is:

$-B < A < B$

In this case:

$-8 < 5 - x < 8$

Step 4: Solve for $x$. Now, solve the inequality by first subtracting 5 from all parts:

$-8 - 5 < -x < 8 - 5$

$-13 < -x < 3$

Finally, multiply through by $-1$ (which reverses the inequality signs):

$13 > x > -3$

This simplifies to:

$-3 < x < 13$

Solution: The solution to the inequality is:

$(-3, 13)$

Would you like any additional details or further clarifications on this?

Related Questions:

1. How do you solve absolute value inequalities with a greater-than condition?
2. What is the rule for reversing inequality signs when multiplying by a negative number?
3. Can you apply this method to inequalities involving more complex expressions?
4. What happens if the absolute value term is already isolated?
5. How do you interpret the solution to an absolute value inequality graphically?

Tip:

Always remember to reverse the inequality sign when multiplying or dividing by a negative number during your steps!