How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

Solution:

The given can be simplified as follows:

12x + 1 = 3(4x + 1) - 2

12x + 1 = 12x + 3 - 2

The 12x term on both sides get cancelled and we are left with

1 = 1

The above identity is true but there is no inference that can be drawn from the above as the variable x is missing. Hence the algebraic expression has no solution.

It is further stated that a system of linear equations is said to be consistent if it has either one solution or infinitely many solutions; a system is inconsistent if it has no solution. This seems to be the case of the equation given in the problem statement. It is inconsistent.

Hence the given equation has no solution.

How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

Summary:

There is no solution that exists for the given equation i.e. 12x + 1 = 3(4x + 1) - 2.