Point N is on line segment \overline{MO} MO . Given MN=2x, MN=2x, NO=x-2,NO=x−2, and MO=2x+9,MO=2x+9, determine the numerical length of \overline{MN}. MN

MN = 22

Explanation:

Given that,

Point N is on line segment MO. MN = 2x, NO = x-2 and MO = 2x+9

ATQ,

MO = NO + MN

Putting all the values,

2x+9=x-2+2x

2x+9=3x-2

Taking like terms together,

2x-3x=-9-2

-x=-11

or

x = 11

Since, MN = 2x

= 2(11)

=22

So, the length of MN is 22 units.

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