Question

if $pq = 2$, $qr=x + 1$, and $pr = 4x$, what is $qr$?
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 $4x=2+(x + 1)$.

Step2: Simplify right - hand side

$4x=2+x + 1$, which simplifies to $4x=x + 3$.

Step3: Isolate x terms

Subtract $x$ from both sides: $4x−x=x + 3−x$, so $3x=3$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{3}{3}$, giving $x = 1$.

Step5: Find QR

Substitute $x = 1$ into the expression for $QR$. Since $QR=x + 1$, then $QR=1 + 1=2$.

Answer:

2