Give an explanation on how many solutions this equation has? 5x + 5 = 5x + 4
Let's analyze the given equation:
5x + 5 = 5x + 4
The usual method to solve an equation is to isolate the variable on one side of the equation. However, before doing that, you can simplify the equation by subtracting '5x' from both sides to try to isolate the x term. When you do this, you get:
5x + 5 - 5x = 5x + 4 - 5x
0 + 5 = 0 + 4
5 = 4
After canceling out the '5x' terms on both sides, you are left with a statement that says 5 equals 4, which is a false statement. Since no value of x can make this equation true (5 will never equal to 4), the equation has no solution. This is an example of an inconsistent equation.
In terms of the number of solutions, this equation has zero solutions. It is important to note that the lack of a solution indicates that the equation is inconsistent and there is no possible value for x that can satisfy the equation.