Question

on a line segment, s is between r and t. if rs = x - 1, st = 8, and rt = 2x - 10, what is rt? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the segment addition postulate

Since \(S\) is between \(R\) and \(T\), \(RS + ST=RT\).
Substitute the given expressions: \((x - 1)+8=2x - 10\).

Step2: Simplify the left - hand side

Simplify \((x - 1)+8\) to \(x+7\). So the equation becomes \(x + 7=2x - 10\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(7=x - 10\).
Then add 10 to both sides: \(x=17\).

Step4: Find the length of \(RT\)

Substitute \(x = 17\) into the expression for \(RT\) (\(RT = 2x-10\)).
\(RT=2\times17 - 10\).
First, calculate \(2\times17=34\). Then \(34-10 = 24\).

Answer:

\(24\)