If |x|>5, then then `xin`_____________

Answer

To solve the inequality |x| > 5, we need to determine the values of x that satisfy this condition.

### Step-by-Step Solution:

1. **Understanding the Absolute Value**:
The absolute value |x| represents the distance of x from 0 on the number line. The inequality |x| > 5 means that the distance of x from 0 is greater than 5.

2. **Breaking Down the Inequality**:
The inequality |x| > 5 can be split into two separate inequalities:
- x > 5
- x < -5

3. **Finding the Solution Set**:
- From the first inequality (x > 5), we see that x can take any value greater than 5.
- From the second inequality (x < -5), we see that x can take any value less than -5.

4. **Combining the Results**:
The solution set can be expressed in interval notation. The values of x that satisfy the original inequality |x| > 5 are:
- From negative infinity to -5 (not including -5): (-∞, -5)
- From 5 to positive infinity (not including 5): (5, ∞)

5. **Final Answer**:
Therefore, we can conclude that:
\[ x \in (-\infty, -5) \cup (5, \infty) \]