Question

if $pq = 19x - 13$, $qr = x + 6$, and $pr = 13$, what is $qr$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $PR = PQ+QR$, we substitute the given expressions: $(19x - 13)+(x + 6)=13$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $19x+x-13 + 6=13$, which simplifies to $20x-7 = 13$.

Step3: Solve for $x$

Add 7 to both sides of the equation: $20x-7 + 7=13 + 7$, so $20x=20$. Then divide both sides by 20: $x=\frac{20}{20}=1$.

Step4: Find the value of $QR$

Substitute $x = 1$ into the expression for $QR$. Since $QR=x + 6$, then $QR=1+6=7$.

Answer:

7