To solve these equations, we will simplify each side of the equation and then combine like terms:
1) 6x + 2 - 4x = 2(x + 2)
2x + 2 = 2x + 4
2 = 4
Since 2 does not equal 4, there is no solution to this equation.
2) 8(x + 2) = 5x + 16 + 3x
8x + 16 = 5x + 16 + 3x
8x + 16 = 8x + 16
0 = 0
Since 0 equals 0, this equation has infinitely many solutions.
3) 3(x + 3) = 7 + 3x + 6 - x
3x + 9 = 13 + 2x
x + 9 = 13 + 2
x + 9 = 15
Subtracting 9 from both sides:
x = 6
This equation has one solution, x = 6.