If pm = 2x - 5, pn = 6x, and mn = 5x + 4, what is the value of x?

The required value of x = 3

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

The given three points are collinear to each other and the point P lies somewhere between the end points of the line MN

So, to find the value of x we can use the relation : Sum of Mid segments PM and PN is equal to complete length of the line segment MN

⇒ PN + PM = MN

⇒ 6·x + 2·x - 5 = 5·x + 4

⇒ 8·x - 5·x = 4 + 5

⇒ 3·x = 9

⇒ x = 3

Hence, The required value of x = 3