Question

determining a missing length
t -------(3x - 4)------- s ------- r
(4x + 1) (from t to r)
which expression represents the measure of segment rs?
○ 7x - 3
○ 7x + 5
○ x + 5
○ x - 3

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 \( TS = 3x - 4 \). So, \( RS=(4x + 1)-(3x - 4) \).

Step3: Simplify the expression

Simplify \( (4x + 1)-(3x - 4) \):
\[

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

\]

Answer:

\( \boldsymbol{x + 5} \) (corresponding to the option "x + 5")