Answer:
x = 5
Step-by-step explanation:
You want to find x when B lies on segment AC and AB=4x+9, BC=5x+2, and AC=56.
Setup
The whole is the sum of the parts.
AB +BC = AC
(4x +9) +(5x +2) = 56
9x +11 = 56 . . . . . . . . . . collect terms
Solution
This is a 2-step linear equation. It can be solved in the usual way.
Step 1 -- add the opposite of the constant on the side with the variable.
9x +11 -11 = 56 -11
9x = 45 . . . . . . . . . . simplify
Step 2 -- divide by the coefficient of the variable.
9x/9 = 45/9
x = 5 . . . . . . . . . . simplify
The value of x is 5.
