Final answer:
To find the value of ST, use the fact that T is the midpoint of SU. Set up an equation using the given values and solve for x. Substitute the value of x to find the value of ST.
Step-by-step explanation:
To find the value of ST, we need to use the fact that T is the midpoint of SU. This means that ST is equal to half of the length of SU. We can set up an equation to represent this relationship:
ST = (1/2) * SU
We also have the given values of ST = x + 9 and SU = 3x + 14. Substituting these values into the equation, we get:
x + 9 = (1/2)(3x + 14)
Now we can solve this equation to find the value of ST (x).
To solve the equation, we can start by distributing the (1/2) to the terms inside the parentheses:
x + 9 = (1/2)(3x) + (1/2)(14)
This simplifies to:
x + 9 = (3/2)x + 7
Next, we can subtract x from both sides of the equation to isolate the x term on the right-hand side:
9 = (3/2)x - x + 7
This further simplifies to:
9 = (1/2)x + 7
Now, we can subtract 7 from both sides of the equation to isolate the (1/2)x term:
2 = (1/2)x
To get rid of the fraction, we can multiply both sides of the equation by 2:
4 = x
Hence, the value of ST (x) is 4 + 9 = 13.