Question

If AB=x+4, BC=2x-10, and AC =2x+1, then find the value for x, AB, BC and AC

Answer 1

If A, B and C are collinear, then:

$AB+BC=AC\\\\AB=x+4,\ BC=2x-10,\ AC=2x+1$

substitute:

$(x+4)+(2x-10)=2x+1\\\\(x+2x)+(4-10)=2x+1\\\\3x-6=2x+1\ \ \ |+6\\\\3x=2x+7\ \ \ \ |-2x\\\\x=7\\\\AB=x+4\to AB=7+4=11\\\\BC=2x-10\to BC=2(7)-10=14-10=4\\\\AC=AB+BC\to AC=11+4=15$