# 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.

Math worksheets and

visual curriculum

visual curriculum