Question

segment addition / subtraction (algebra)
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question
point s is on line segment \\(\overline{rt}\\). given \\(st = 5x - 7\\), \\(rt = 4x + 9\\), and \\(rs = 2x + 7\\), determine the numerical length of \\(\overline{st}\\).
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\\(st = \\)
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Explanation:

Step1: Apply segment addition postulate

$RT = RS + ST$

Step2: Substitute given expressions

$4x + 9 = (2x + 7) + (5x - 7)$

Step3: Simplify right-hand side

$4x + 9 = 7x$

Step4: Solve for $x$

$9 = 3x \implies x = 3$

Step5: Calculate $ST$

$ST = 5(3) - 7$

Answer:

$8$