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.