Point Q is on line segment PR given QR equals 3X PQ equals X +6 and PR equals 5X -4 determine the numberical length of PQ

Answer 1

5x-4

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P Q R

x+6 3x

The segment addition postulate states tells us that PQ + QR = PR

So,

x+6 + 3x = 5x-4

combine like terms

4x+6 = 5x-4

And solve the algebraic equation

Subtract 4x from both sides

6 = x-4

Add 4 to both sides

10 = x

PQ = x+6 = 10+6 = 16