To solve the inequality $3|x - 10| + 4 > 10$, follow these steps:

1. Isolate the absolute value expression: $3|x - 10| + 4 > 10$ Subtract 4 from both sides: $3|x - 10| > 6$ Divide both sides by 3: $|x - 10| > 2$

2. Consider the definition of absolute value: The inequality $|x - 10| > 2$ means that the expression inside the absolute value is either greater than 2 or less than -2: $x - 10 > 2 \quad \text{or} \quad x - 10 < -2$

3. Solve each case:

   • For $x - 10 > 2$: $x > 12$
   • For $x - 10 < -2$: $x < 8$

4. Write the solution: The solution is $x > 12$ or $x < 8$.

In interval notation, this is: $x \in (-\infty, 8) \cup (12, \infty)$

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you solve inequalities involving quadratic expressions?
2. What are the steps to graph an absolute value inequality?
3. Can you solve the inequality $2|x + 3| \leq 8$?
4. How does the solution of $|ax + b| > c$ change if $a$ is negative?
5. What is the difference between solving $|x - 5| > 3$ and $|x - 5| < 3$?

Tip: When solving absolute value inequalities, always remember to consider both the positive and negative scenarios inside the absolute value.