D,V and U are collinear with U between D and V. Draw a diagram and solve for x, given: DU=4x+5, VU=3x-8 and VD=10x-6?

1 Answer

#color(blue)(x = 1)#

Explanation:

Given #DU = a = 4x + 5, VU = b = 3x - 8, VD = DU + VU = a + b = 10x - 6#

To find x.

#a + b = 4x + 5 + 3x - 8 = 7x - 3# Eqn (1)

But given #VD = DU + VU = a + b = 10x - 6# Eqn (2)

Equating both (1) , (2),

#7x - 3 = 10x - 6# Rearranging like terms together,

#10x - 7x = 6 - 3#

#3x = 3# or #x = 1#