Question

determining a missing length
which expression represents the measure of segment rs?
7x - 3
7x + 5
x + 5
x - 3

Explanation:

Step1: Identify the relationship

We know that $TR=TS + RS$. Given $TR = 4x + 1$ and $TS=3x - 4$. Let $RS=y$. Then $4x + 1=(3x - 4)+y$.

Step2: Solve for $RS$

We can solve the equation $4x + 1=(3x - 4)+y$ for $y$ (which is $RS$). Rearranging the equation gives $y=(4x + 1)-(3x - 4)$.
Expand the right - hand side: $y = 4x+1 - 3x + 4$.
Combine like terms: $y=(4x-3x)+(1 + 4)=x + 5$.

Answer:

C. $x + 5$