Question

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, we can find \( RS \) by subtracting \( TS \) from \( TR \). Given \( TR = 4x + 1 \) and \( TS = 3x - 4 \), we calculate \( RS = TR - TS \).

Step2: Substitute the expressions

Substitute \( TR = 4x + 1 \) and \( TS = 3x - 4 \) into the formula:

$$ RS=(4x + 1)-(3x - 4) $$

Step3: Simplify the expression

Simplify the right - hand side by distributing the negative sign and combining like terms:

$$
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$$

Answer:

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