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When solving an equation, there are three possible outcomes: no solution, infinitely many solutions (also known as an identity), and a solution of zero. Here’s what each of these outcomes means:
No solution: An equation with no solution means that there is no value of the variable that makes the equation true. For example, the equation x + 1 = x + 2 has no solution because there is no value of x that makes the left side equal to the right side.
Infinitely many solutions (identity): An equation with infinitely many solutions means that any value of the variable makes the equation true. In other words, the equation is always true, regardless of the value of the variable. For example, the equation x = x is an identity because it is always true, no matter what value of x you choose.
Solution of zero: An equation with a solution of zero means that there is exactly one value of the variable that makes the equation true, and that value is zero. For example, the equation x + 2 = 2 has a solution of zero because x must be equal to zero in order for the equation to be true.
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