Point m is the midpoint of segment ab. if am = 2x + 5 and mb = 5x – 22, find the value of x.

Having point M as midpoint of segment AB, it only shows that the length of AM is equal to the length MB. Hence, AM = MB

AM = MB
2x + 5 = 5x - 22      ⇒ substitute the values
5 + 22 = 5x - 2x      ⇒ combine like terms
27 = 3x                   ⇒ simplify and divide both sides by 3 to get the value of x
x = 9                       ⇒ Answer