To solve the inequality \( |x| + 5 > 10 \), we can follow these steps:

### Step 1: Isolate the absolute value
First, subtract 5 from both sides of the inequality:
\[
|x| > 10 - 5
\]
\[
|x| > 5
\]

### Step 2: Remove the absolute value
The expression \( |x| > 5 \) means that \( x \) can be either greater than 5 or less than -5. So, we split it into two inequalities:
\[
x > 5 \quad \text{or} \quad x < -5
\]

### Solution
The solution to the inequality is:
\[
x > 5 \quad \text{or} \quad x < -5
\]

In interval notation, the solution is:
\[
(-\infty, -5) \cup (5, \infty)
\]

Would you like more details on any step?

### 5 Related Questions:
1. How do you solve inequalities with multiple absolute values?
2. What are the rules for solving inequalities with absolute values?
3. Can you solve \( |2x - 3| > 7 \)?
4. What is the difference between \( |x| > a \) and \( |x| < a \)?
5. How do you graph the solution to \( |x| + 5 > 10 \)?

### Tip:
Always remember that when you remove the absolute value, you must consider both the positive and negative cases of the expression inside the absolute value.

Learn how to solve the absolute value inequality |x| + 5 > 10 with a step-by-step explanation. This problem focuses on isolating the absolute value and solving inequalities for both positive and negative cases. Suitable for students in Grades 8-10.

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