Question

1. if q is the midpoint of $overline{pr}$, find the value of x.

$7x - 16$ $4x + 2$
p q r

Explanation:

Step1: Set up the equation

Since Q is the mid - point of $\overline{PR}$, then $PQ = QR$. So, $7x−16 = 4x + 2$.

Step2: Isolate the variable terms

Subtract $4x$ from both sides of the equation:
$7x−4x−16=4x−4x + 2$, which simplifies to $3x−16 = 2$.

Step3: Isolate the variable

Add 16 to both sides of the equation:
$3x−16 + 16=2 + 16$, so $3x=18$.

Step4: Solve for x

Divide both sides of the equation by 3:
$\frac{3x}{3}=\frac{18}{3}$, so $x = 6$.

Answer:

$x = 6$