Answer: 0 is a real number, and the only equation that gives us the solution of x to be zero are equation 1 and equation 4
The first equation is given as
4(3 - x) + 7x = 4x + 12 + 2x
Firstly, we need to open the parenthesis
4*3 - 4*x + 7x = 4x + 12 + 2x
12 - 4x + 7x = 4x + 12 + 2x
Collect the like terms
12 - 12 = 4x + 2x + 4x - 7x
0 = 10x - 7x
0 = 3x
Divide both sides by 3
0/3 = 3x/3
x = 0
For the second equation
3(4 - x) + 6x = 4x + 12 - x
Open the parenthesis
3*4 - 3*x + 6x = 4x + 12 - x
12 - 3x + 6x = 4x + 12 - x
Collect the like terms
12 - 12= 4x - x + 3x - 6x
0 = 6x - 6x
0 = 0......... No solution
Third equation
4(3 - x) + 6x = 3x + 8 - x
Open the parenthesis
4*3 - 4*x + 6x = 3x + 8 - x
Collect the like terms
12 - 4x + 6x = 3x + 8 - x
12 + 2x = 3x - x + 8
Collect the like terms
12 - 8 = 2x - 2x
4 = 0x
x = infinity
Fourth equation
4(4 - x) + 6x = x + 16 - 4x
Open the parenthesis
16 - 4x + 6x = x + 16 - 4x
16 + 2x = x - 4x + 16
16 - 16 = x - 4x - 2x
0 = -3x - 2x
0 = -5x
Divide both sides by -5
0/-5 = -5x / -5
x = 0
0 is a real number, and the only equation that gives us the solution of x to be zero are equation 1 and equation 4