The value of x is approximately 27.
To solve for x in the given image, we can use the following steps:
Identify the type of triangle.
The triangle in the image is a right triangle, since one of its angles is 90 degrees.
7x + 6 = 114
7x = 114 - 6
7x = 108
x = 108/7
x = 15.43.
Therefore, the value of x is approximately 15.43.