Simplify each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. Explain your answers.

(a) 6x + 2 (2x - 3) = 24 + 9x

(b) 25 - 4x = 3 (5 - x) + 10 - x

(c) 4 (x + 2) = 2x + 7 + 2 (x - 10)

A) The answer is one solution, neither

6x + 2 (2x - 3) = 24 + 9x

6x + 2 * 2x + 2 * (-3) = 24 + 9x

6x + 4x - 6 = 24 + 9x

10x - 6 = 24 + 9x

10x - 9x = 24 + 6

x = 30

b) The answer is infinity solutions, identity

25 - 4x = 3 (5 - x) + 10 - x

25 - 4x = 3 * 5 - 3 * x + 10 - x

25 - 4x = 15 - 3x + 10 - x

25 - 4x = 25 - 4x

4x - 4x = 25 - 25

0x = 0

x can be any number, so an infinite number of solution

c) The answer is no solution, contradiction

4 (x + 2) = 2x + 7 + 2 (x - 10)

4 * x + 4 * 2 = 2x + 7 + 2 * x - 2 * 10

4x + 8 = 2x + 7 + 2x - 20

4x + 8 = 4x - 13

4x - 4x = - 8 - 13

0 = - 13

this is contradiction