Point Q is on line segment \overline{PR} PR . Given QR=3x,QR=3x, PQ=x+6,PQ=x+6, and PR=5x-4,PR=5x−4, determine the numerical length of \overline{PQ}. PQ ​ .

Question

Point Q is on line segment PR. Given QR=3x, PQ=x+6, and PR=5x−4, determine the numerical length of PQ​.

Answer 1

We are given:

QR = 3x

PQ = x + 6

PR = 5x - 4

We need to come up with an equation that relates QR, PQ, and PR so that we can solve for x.

If we draw a line PR with a point Q somewhere in the middle, we can see that QR and PQ together make up PR. Therefore,

QR + PQ = PR

We can now substitute the given information for each of the line segments:

(3x) + (x + 6) = (5x - 4)

3x + x + 6 = 5x - 4

4x + 6 = 5x - 4

4x + 10 = 5x

10 = x

So we know x = 10, but we're not done yet, since we're asked to find the length of PQ. We can fill in x = 10 into the equation for PQ:

PQ = x + 6

PQ = 3 + 6

PQ = 9