Question

P, Q, and R are collinear points with Q between P and R. PQ=4x+7, QR=5x+11, and PR=54. Use the Segment Addition Postulate to solve for x.

Answer 1

This problem is about the sum of segments.

We know that

PR = 54 (the total length of the segment)

PQ = 4x + 7

QR = 5x + 11

By the segment addition postulate, we can say that

$PR=PQ+QR$

Replacing the given information, we have

$54=4x+7+5x+11$

Now, we solve for x

$54-7-11=4x+5x\rightarrow9x=36$

Then, we divide the equation by 9

$\frac{9x}{9}=\frac{36}{9}\rightarrow x=4$

Therefore, the value of x is 4.