Point M is on line segment \overline{LN} LN . Given LN=4x,LN=4x, MN=x,MN=x, and LM=3,LM=3, determine the numerical length of \overline{LN}. LN .

Answer 1

Because M is a point on a straight line between L and N, the shorter distance LM plus the shorter distance MN must equal the longer distance LN. (This is because there is no shorter distance between two point then a straight line.)

LM = 3

+ MN = x

__________

LN = 4x

So we get the equation: 3 + x = 4x

Then just solve for x.