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Point N is on line segment M O ‾ MO . Given N O = 2 x − 3 , NO=2x−3, M O = 3 x + 5 , MO=3x+5, and M N = 2 x + 3 , MN=2x+3, determine the numerical length of M O ‾ . MO .

Respuesta :

Answer: The length of MO is 20 units.

Explanation:

It is given that Point N is on line segment M O.

Using segment addition property, we get

[tex]MO=MN+NO[/tex]

Given values are NO=2x−3, MO=3x+5, and MN=2x+3.

[tex]3x+5=(2x+3)+(2x-3)[/tex]

[tex]3x+5=4x[/tex]

[tex]5=4x-3x[/tex]

[tex]5=x[/tex]

The value of x is 5.

[tex]MO=3x+5[/tex]

[tex]MO=3(5)+5[/tex]

[tex]MO=15+5[/tex]

[tex]MO=20[/tex]

Therefore, the length of MO is 20 units.

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