Find x

Is the triangle equilateral, isosceles, or scalen, and explain.
The picture is a circle with a triangle inside P at the top and Q left corner and R at right corner it's labeled with (8x-10) on the outside of the circle between QP, and (6x) on the outside of triangle PR, then at the bottom its (10x+10) between QR
hope this helps because i really need help

To determine the type of triangle (equilateral, isosceles, or scalene) and find the value of x, we need to examine the provided values in the given diagram.

Let's start by analyzing the triangle based on the given information:

1. Side QP: The length of the line segment between points Q and P is (8x - 10).
2. Side PR: The length of the line segment between points P and R is (6x).
3. Side QR: The length of the line segment between points Q and R is (10x + 10).

To determine the triangle type, we need to consider the lengths of the sides:
- An equilateral triangle has all three sides equal in length.
- An isosceles triangle has two sides equal in length.
- A scalene triangle has all three sides of different lengths.

Now, let's compare the lengths of the sides:
1. Compare sides QP and PR:
(8x - 10) ≠ (6x), as the lengths are not equal.

Since sides QP and PR are not equal in length, we can conclude that the triangle is not equilateral.

2. Compare sides QP and QR:
(8x - 10) ≠ (10x + 10), as the lengths are not equal.

Since sides QP and QR are not equal in length, we can conclude that the triangle is not isosceles either.

By the process of elimination, we can determine that the triangle must be scalene since none of its sides are equal in length.

To find the value of x, we can equate any two side lengths and solve the resulting equation. Let's equate sides PR and QR:

(6x) = (10x + 10)
6x - 10x = 10
-4x = 10
x = -10/4
x = -5/2

Therefore, the value of x is -5/2.

In summary, based on the provided information, the triangle is determined to be scalene, and the value of x is -5/2.