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.

Learn how to solve the absolute value inequality 3|x - 10| + 4 > 10 step-by-step. This problem involves inequalities, absolute values, and algebraic manipulations. Suitable for students in Grades 9-12.

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