If ab=x+3,bc=2x and ac=4x-5.then for which value of x,b lies on ac?
If b lies on ac, then ab+bc = ac
x+3 + 2x = 4x-5
x = 8
To find the value of x for which point B lies on line segment AC, we need to look at the relationship between the coordinates of points A, B, and C.
We know that AB + BC = AC, which means that the length of line segment AB added to the length of line segment BC should be equal to the length of line segment AC.
Given:
AB = x + 3
BC = 2x
AC = 4x - 5
Substituting the given values into the equation AB + BC = AC, we get:
(x + 3) + (2x) = 4x - 5
Simplifying the equation:
3x + 3 = 4x - 5
Subtracting 3x from both sides of the equation:
3 = x - 5
Adding 5 to both sides of the equation:
8 = x
Therefore, for x = 8, point B lies on line segment AC.