Question

10 q is the midpoint $overline{pr}$, find the value of x. $7x - 16$ $4x + 2$ p q r (a) $x = -\frac{11}{14}$ (b) $x = -6$ (c) $x = 6$ (d) $x = 18$

Explanation:

Step1: Use mid - point property

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

Step2: Isolate x terms

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

Step3: Isolate the constant

Add 16 to both sides: $3x−16 + 16=2 + 16$, getting $3x=18$.

Step4: Solve for x

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

Answer:

C. $x = 6$