(a) 2x + 3x - 6 = 10 + 4x ---> Answer: x = 16, it has one solution, it is an identity.
Adding the like terms on the same side of the equation to solve for x:
2x + 3x - 4x = 10 + 6
x = 16
(b) 17 + 5x = 23 + 4x - 6 + x ---> Answer: it has infinite number of solutions, it is a contradiction
Adding the like terms on the same side of the equation to solve for x:
5x - 4x - x = 23 - 17 - 6
5x - 5x = 6 - 6 (this equation is cancelling everything on each side so it can not be true no matter what value we assign, therefore it has infinite number of solution)
(c) 7x + 4 = 5x + 8 + 2x - 10 ---> Answer: no solution, its a contradiction.
Adding the like terms on the same side of the equation to solve for x:
7x - 5x - 2x = -10 + 8 - 4
7x - 7x = -6 (the terms of x are cancelled by each other, therefore no solution.
