Question

if (pq = 2x), (qr=x + 1), and (pr = 10), what is (pq)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation

Since $PR = PQ+QR$, we have $2x+(x + 1)=10$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $3x+1 = 10$.

Step3: Isolate the variable term

Subtract 1 from both sides: $3x=10 - 1$, so $3x=9$.

Step4: Solve for $x$

Divide both sides by 3: $x=\frac{9}{3}=3$.

Step5: Find $PQ$

Since $PQ = 2x$, substitute $x = 3$ into the expression for $PQ$. So $PQ=2\times3 = 6$.

Answer:

6