Respuesta :
a. 4(3-x) + 6x = 3x + 12 - x
12 - 4x + 6x = 2x + 12
2x + 12 = 2x + 12...infinite solutions <=== this one
b. 4(3 - x) + 6x = 3x + 10 - x
12 - 4x + 6x = 2x + 10
2x + 12 = 2x + 10...not this one...no solutions
c. 4(3 - x) + 6x = 3x + 12 + 2x
12 - 4x + 6x = 5x + 12
2x + 12 = 5x + 12....not this one...one solution
d. 4(3 - x) + 6x = x + 12 - 3x
12 - 4x + 6x = -2x + 12
2x + 12 = -2x + 12...not this one...one solution
12 - 4x + 6x = 2x + 12
2x + 12 = 2x + 12...infinite solutions <=== this one
b. 4(3 - x) + 6x = 3x + 10 - x
12 - 4x + 6x = 2x + 10
2x + 12 = 2x + 10...not this one...no solutions
c. 4(3 - x) + 6x = 3x + 12 + 2x
12 - 4x + 6x = 5x + 12
2x + 12 = 5x + 12....not this one...one solution
d. 4(3 - x) + 6x = x + 12 - 3x
12 - 4x + 6x = -2x + 12
2x + 12 = -2x + 12...not this one...one solution
The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.
Check all the options in order to determine which of the following equations has the solution x = all real numbers.
A) 4(3 - x) + 6x = 3x + 12 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 3x + 12 - x
= 2x + 12
LHS = RHS means there is an infinite number of solutions.
B) 4(3 - x) + 6x = 3x + 10 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 2x + 10
LHS [tex]\neq[/tex] RHS means that there are no solutions.
C) 4(3 - x) + 6x = 3x + 12 + 2x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 5x + 12
LHS [tex]\neq[/tex] RHS means that there are no solutions.
D) 4(3 - x) + 6x = x + 12 - 3x
Simplify the above equation separately that is:
LHS = 12 + 2x
RHS = 12 - 2x
LHS [tex]\neq[/tex] RHS means that there are no solutions.
For more information, refer to the link given below:
https://brainly.com/question/13911928
