Question

Point O is on line segment \overline{NP}

NP
. Given OP=4x-5,OP=4x−5, NP=3x+4,NP=3x+4, and NO=2x-3,NO=2x−3, determine the numerical length of \overline{OP}.
OP
.

Answer 1

`OP = 11`

Explanation:

Given

OP = 4x - 5

NP = 3x + 4

NO = 2x - 3

Required

Determine the value of OP

Since O lines n the segment, them

`NP = NO+ OP\\`

`3x + 4 = 2x - 3 + 4x - 5`

Collect Like Terms

`3x - 2x - 4x = -3 -5 - 4`

`-3x=-12`

`x = (-12)/(-3)`

`x = 4`

Substitute 4 for x in OP = 4x - 5

`OP = 4 * 4 - 5`

`OP = 16 - 5`

`OP = 11`