Answer: 11 units.
Step-by-step explanation:
Given: Point O is on line segment NP.
i.e. NP is the combination of NO and OP.
i.e. NP = NO+OP (1)
Since , OP = 4x - 5 , NP = 3x + 4 , and NO = 2x - 3
Substitute these values in (1), we get
[tex]3x + 4 = 2x - 3 + 4x - 5[/tex]
[tex]\Rightarrow\ 3x+4=2x+4x-3-5\\\\\Rightarrow\ 3x+4=6x-8\\\\\Rightarrow\ 6x-3x=8+4\\\\\Rightarrow\ 3x=12\\\\\Rightarrow\ x=\dfrac{3}{12}=4[/tex]
i.e. x= 4
Now, OP = 4(4)-5= 16-5= 11 units
Hence, the numerical length of OP is 11 units.
