Final answer:
To find the inequality that represents the possible values of x in the triangle RST, we use the triangle inequality theorem. Using the given side lengths, we form the inequality (x+15)+(8x-26)>(3x+1). Solving this inequality, we find x>11/6.
Step-by-step explanation:
To find the inequality that shows all the possible values of x in the triangle RST, we need to consider the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, RS+ST>RT, so we can write the inequality (x+15)+(8x-26)>(3x+1). Now we can solve this inequality to find the possible values of x.
Expanding and simplifying the inequality, we get 9x-10>3x+1.
Subtracting 3x from both sides and adding 10 to both sides, we get 6x>11.
Dividing both sides by 6, we find that x>11/6.
The inequality that shows all the possible values of x is x>11/6.