Question

1. find pq.

38
p x + 5 q 2x r

Explanation:

Step1: Set up equation based on segment - addition postulate

Since $PR = PQ+QR$ and $PR = 38$, $PQ=x + 5$, $QR = 2x$, we have the equation $x + 5+2x=38$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side, we get $3x+5 = 38$.

Step3: Isolate the variable term

Subtract 5 from both sides of the equation: $3x+5−5=38 - 5$, which simplifies to $3x=33$.

Step4: Solve for $x$

Divide both sides of the equation $3x = 33$ by 3: $\frac{3x}{3}=\frac{33}{3}$, so $x = 11$.

Step5: Find $PQ$

Substitute $x = 11$ into the expression for $PQ$. Since $PQ=x + 5$, then $PQ=11 + 5=16$.

Answer:

16