Answer:
RS = 6 units
Step-by-step explanation:
You want the length of segment RS when it is 1/3 of the length of RT and the lengths are given by the expressions RS=3x-3 and ST=2x+6.
Setup
Using the given expressions, we can write an equation for segment RS.
RS = 1/3(RS +ST)
3x -3 = 1/3((3x -3) +(2x +6))
Solution
Multiplying by 3 and simplifying, we get ...
9x -9 = 5x +3
4x = 12
x = 3
RS = 3x -3 = 3·3 -3 = 6
The length of RS is 6 units.
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Additional comment
The length of ST is 2(3) +6 = 12, and the length of RT is 6+12 = 18.
