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T is the midpoint of su. if st=x 9 and su = 3x 14 what is st?

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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.

User Rob Kraft
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