Question

Point I is on line segment start overline, H, J, end overline
HJ
. Given H, I, equals, x, commaHI=x, H, J, equals, 3, x, minus, 9, commaHJ=3x−9, and I, J, equals, x, plus, 5, commaIJ=x+5, determine the numerical length of start overline, H, J, end overline, .
HJ
.

Answer 1

Since I is between H and J, HJ = HI + IJ.

So 3x − 9 = x + (x + 5) = 2x + 5.
Solve: 3x − 9 = 2x + 5 ⇒ x = 14.

Then HJ = 3x − 9 = 3(14) − 9 = 42 − 9 = 33.

Answer: HJ = 33.