Question

r is a point on segment $overline{qs}$. if $qr = 7x$, $rs = x + 11$, and $qs = 19$, what is $qr$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $R$ is on segment $\overline{QS}$, then $QR + RS=QS$. Substitute the given expressions: $7x+(x + 11)=19$.

Step2: Combine like - terms

Combine the $x$ terms on the left - hand side: $7x+x+11 = 19$ becomes $8x+11 = 19$.

Step3: Isolate the variable term

Subtract 11 from both sides of the equation: $8x+11−11=19 - 11$, so $8x=8$.

Step4: Solve for $x$

Divide both sides by 8: $\frac{8x}{8}=\frac{8}{8}$, so $x = 1$.

Step5: Find $QR$

Substitute $x = 1$ into the expression for $QR$. Since $QR = 7x$, then $QR=7\times1=7$.

Answer:

7