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An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
They each typically have two solutions, a positive one and a negative one.
A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.
One solution: x = -4
One.