Sketch the region satisfying `|x| lt |y|`.

Explanation

To sketch the region satisfying the inequality \( |x| < |y| \), we can follow these steps:

### Step 1: Understand the Inequality
The inequality \( |x| < |y| \) means that the absolute value of \( x \) is less than the absolute value of \( y \). This implies that the distance of \( y \) from the origin must be greater than the distance of \( x \) from the origin.

### Step 2: Set Up the Boundary Lines
To find the boundary of the region defined by the inequality, we first consider the equality \( |x| = |y| \). This can be broken down into four cases:
1. \( y = x \)
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