Question

point r is on line segment $overline{qs}$. given $qr = 3x - 8, qs = 3x$, and $rs = 2x$, determine the numerical length of $overline{rs}$. answer attempt 1 out of 2 $rs=$

Explanation:

Step1: Use segment - addition postulate

Since point R is on line segment $\overline{QS}$, we have $QR + RS=QS$. Substitute the given expressions: $(3x - 8)+2x = 3x$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x-8 + 2x=5x - 8$. So, $5x-8 = 3x$.

Step3: Solve for x

Subtract $3x$ from both sides: $5x-3x-8=3x - 3x$, which gives $2x-8 = 0$. Then add 8 to both sides: $2x-8 + 8=0 + 8$, so $2x=8$. Divide both sides by 2: $x = 4$.

Step4: Find the length of RS

We know that $RS = 2x$. Substitute $x = 4$ into the expression for $RS$. So, $RS=2\times4=8$.

Answer:

$8$