To solve the problem, we must use the property of an equilateral triangle: all sides are equal in length.

The sides of the triangle are labeled as:

1. $2x - 5$,
2. $19$,
3. (implicitly) $19$, as it’s an equilateral triangle.

Step-by-step solution:

Since all sides are equal in an equilateral triangle:

$2x - 5 = 19$

Now, solve for $x$:

1. Add 5 to both sides: $2x = 24$

2. Divide both sides by 2: $x = 12$

Final Answer:

$x = 12$

Would you like me to explain any part in more detail or verify with another approach?

Here are 5 related questions for further practice:

1. What are the properties of an equilateral triangle?
2. How do you verify if a triangle is equilateral using side lengths?
3. If $x = 12$, what are the lengths of all sides of this triangle?
4. How would the solution change if the triangle were isosceles instead?
5. How can this concept be applied in coordinate geometry for triangles?

Tip: Always write down what is given and identify the properties of