Question

if pq = x + 1, qr = 6, and pr = 7x - 17, what is pr?
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 have the equation $7x - 17=(x + 1)+6$.

Step2: Simplify the right - hand side of the equation

$(x + 1)+6=x+7$. So the equation becomes $7x-17=x + 7$.

Step3: Isolate the variable terms

Subtract $x$ from both sides: $7x-x-17=x - x+7$, which simplifies to $6x-17 = 7$.

Step4: Isolate the variable term with $x$

Add 17 to both sides: $6x-17 + 17=7 + 17$, so $6x=24$.

Step5: Solve for $x$

Divide both sides by 6: $\frac{6x}{6}=\frac{24}{6}$, and $x = 4$.

Step6: Find the value of $PR$

Substitute $x = 4$ into the expression for $PR$: $PR=7x-17$. Then $PR=7\times4-17$.
$PR = 28-17$.
$PR = 11$.

Answer:

11