Answer:
(a) 5x + 9 = 2x + 7 + 3x - 15
combine like terms
5x + 9 = 5x - 8
subtract 5x and 9 from both sides
0 = -17
This statement is false, so there are no solutions. This is a contradiction equation.
(b) 7x + 5x - 7 = 21 + 10x
combine like terms
12x - 7 = 21 + 10x
subtract 10x from both sides and add 7 to both sides
2x = 28
divide by 2
x = 14
neither - it's a conditional equation
(c) 24 - 3x = 8 - 2x + 16 - x
combine like terms
24 - 3x = 24 - 3x
This equation is true and will always be true no matter what x value is plugged in. There are an infinite number of solutions. This is an identity equation.