Point m lies between points l and n on line segment l n .

the space between l and m is 10 x + 8. the space between m and n is 5 x minus 4.
if ln = 12x + 16, what is the length of line segment l n in units?

16 units
40 units
48 units
64 units

64 units

Step-by-step explanation:

Given:

Point M lies between points L and N on Line segment LN.

Length of segment LM is given as =

Length of segment MN is given as =

Length of segment LN is given as =

From the information given we can conclude that the points L,M and N ar co-linear and

    [ Segment addition postulate as M lies in between L and N]

Substituting the values given to find .

Combining like terms.

Subtracting both sides by

Subtracting both sides by 4.

Dividing both sides by 3.

∴

Length of segment LN can be found out by substituting in the expression for segment.

⇒

⇒

⇒

Length of segment LN = 64 units (Answer)