Question

determining a missing length
which expression represents the measure of segment rs?
○ 7x−3
○ 7x+5
○ x+5
○ x−3
(diagram: points t, s, r on a line; ts labeled ( 3x - 4 ), tr labeled ( 4x + 1 ))

Explanation:

Step1: Recall segment addition postulate

The segment addition postulate states that if \( S \) is between \( T \) and \( R \), then \( TR = TS + SR \). So, \( RS=TR - TS \).

Step2: Substitute the given expressions

We know \( TR = 4x + 1 \) and \( TS=3x - 4 \). Then \( RS=(4x + 1)-(3x - 4) \).

Step3: Simplify the expression

\[

$$\begin{align*} RS&=4x + 1-3x + 4\\ &=(4x-3x)+(1 + 4)\\ &=x+5 \end{align*}$$

\]

Answer:

\( x + 5 \) (corresponding to the option with this expression)