Point N is on line segment \overline{MO}

MO
. Given MO=3x+6,MO=3x+6, NO=5x,NO=5x, and MN=x,MN=x, determine the numerical length of \overline{NO}.
NO
.

wow - what a lot of repeated gobbledegook!

Since MN+NO = MO, you have
x + 5x = 3x+6
now finish it off

5

2

To determine the numerical length of line segment NO, we need to determine the value of x first.

We know that N is on line segment MO, which means that the sum of lengths MN and NO is equal to MO.

So, we can write the equation:

MN + NO = MO

Substituting the given lengths, we have:

x + (5x) = 3x + 6

Simplifying the equation further:

6x = 3x + 6

Now, let's isolate the variable x:

6x - 3x = 6

3x = 6

Dividing both sides by 3:

x = 2

Now that we have the value of x, we can substitute it back into the expression for NO to find its numerical length.

NO = 5x = 5(2) = 10

Therefore, the numerical length of line segment NO is 10.