In the scenario described, you have an equation of the form \( a = b \) with the same number of \( x \)'s (variables) on both sides and different constants (i.e., \( c_1 \neq c_2 \)). This means that when you simplify or solve the equation, you will ultimately arrive at a contradiction.
Since both sides are equal (same expressions with \( x \)), but when simplified will yield an equation such as \( c_1 = c_2 \) where \( c_1 \) and \( c_2 \) are not equal, there are no possible values of \( x \) that can satisfy the equation.
Thus, the number of solutions for this type of equation is zero solutions.
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