Which statement correctly describes the solution to the equation below?

-4[x+2]+x = 3x - 8 - 5x

A There is no solution to this equation.

B There are infinitely many solutions to this equation.

C There is exactly one solution to this equation, and the solution is 0.

D There is exactly one solution to this equation, and the solution is - 1.

Option C) There is exactly one solution to this equation, and the solution is 0 is correct

That is the solution x=0

Step-by-step explanation:

Given equation is - 4 (x+2) + x=3x-8-5x

To find the solution to the given equation:

First to solve the given equation

-4 (x+2) + x=3x-8-5x

-4x-8+x=3x-8-5x (by using the distributive property)

-3x-8=-2x-8 (adding the like terms)

-3x-8 - (-2x-8) = -2x-8 - (-2x-8)

-3x-8+2x+8=-2x-8+2x+8 (adding the like terms)

-x=0

Therefore x=0 is the only solution to the given equation

Option C) There is exactly one solution to this equation, and the solution is 0 is correct

That is the solution x=0