If AB = x + 3, BC = 2x, and AC = 4x - 5, then for what value of 'x' does B lie on AC?

Explanation

For point B to lie on line AC, the sum of AB and BC must equal AC. Therefore, we have: AB + BC = AC Substitute the given values: (x + 3) + (2x) = 4x - 5 Simplify the equation: x + 3 + 2x = 4x - 5 3x + 3 = 4x - 5 Now, isolate x by moving terms involving x to one side and constants to the other side: 3 + 5 = 4x - 3x 8=x Therefore, the value of x that satisfies the condition is 8.