Question

r is the midpoint of $overline{qs}$. if $qr = 8x$ and $qs = 14x + 10$, what is $qr$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $R$ is the mid - point of $\overline{QS}$, then $QR=\frac{1}{2}QS$. So, $2QR = QS$.

Step2: Substitute given expressions

Substitute $QR = 8x$ and $QS=14x + 10$ into $2QR = QS$. We get $2\times8x=14x + 10$.

Step3: Simplify the equation

$16x=14x + 10$. Subtract $14x$ from both sides: $16x-14x=14x + 10-14x$, which gives $2x=10$.

Step4: Solve for $x$

Divide both sides of $2x = 10$ by 2: $x=\frac{10}{2}=5$.

Step5: Find $QR$

Substitute $x = 5$ into the expression for $QR$. Since $QR = 8x$, then $QR=8\times5 = 40$.

Answer:

40