Question

point t is on line segment (overline{su}). given (st = 2x + 1), (su = 4x), and (tu = 5x - 4), determine the numerical length of (overline{st}).

Explanation:

Step1: Use segment addition postulate

Since \(ST + TU=SU\), substitute the given expressions: \((2x + 1)+(5x - 4)=4x\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+5x + 1-4=4x\), so \(7x - 3=4x\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(7x-4x - 3=4x-4x\), \(3x-3 = 0\). Then add \(3\) to both sides: \(3x=3\), and divide by \(3\): \(x = 1\).

Step4: Find the length of \(ST\)

Substitute \(x = 1\) into \(ST=2x + 1\). So \(ST=2(1)+1\).

Answer:

\(3\)