HJ=5x−3 , JK=8x−9, and KH=131 Find: x, HJ, and JK

Question

Segment Addition Postulate

Answer 1

The sum of the lengths of the two segments HJ and JK equals the length of KH

(5x-3) + (8x-9) = 131

13x - 12 = 131 combine like terms

+12 +12 add 12 to both sides

13x = 143 simplify

/13 /13 divide by 13 on both sides

x = 11

substitute 11 for x in the two original segments

HJ = 5x - 3 = 5 (11) - 3 = 55 - 3 = 52

JK = 8x - 9 = 8(11) - 9 = 88 - 9 = 79