To find the area of the triangular region bounded by the lines $y = 2x$, $y = -2x$, and $x = 5$, we can follow these steps:

1. Determine the vertices of the triangle:

   • The line $y = 2x$ intersects $x = 5$ at the point $(5, 10)$.
   • The line $y = -2x$ intersects $x = 5$ at the point $(5, -10)$.
   • The two lines $y = 2x$ and $y = -2x$ intersect at the origin $(0, 0)$.

   So, the vertices of the triangle are $(0, 0)$, $(5, 10)$, and $(5, -10)$.

2. Calculate the base and height of the triangle:

   • The base of the triangle is the vertical distance between the points $(5, 10)$ and $(5, -10)$, which is $10 - (-10) = 20$ units.
   • The height of the triangle is the horizontal distance from the origin $(0, 0)$ to the line $x = 5$, which is 5 units.

3. Use the formula for the area of a triangle:

   The area $A$ of a triangle is given by:

   $A = \frac{1}{2} \times \text{base} \times \text{height}$

   Substituting the values we found:

   $A = \frac{1}{2} \times 20 \times 5 = 50 \text{ square units}$

So, the number of square units in the triangular region is 50.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do we find the area of a triangle given its vertices?
2. How does the slope of a line affect the shape of a triangle formed with it?
3. What is the significance of the intersection points of these lines?
4. How would the area change if the lines intersected at a different x-coordinate?
5. How can we generalize this problem to any set of linear equations forming a triangle?

Tip: The area of a triangle can be quickly found using the determinant method if the coordinates of its vertices are known.