Here are the essential concepts you must grasp in order to answer the question correctly.
Identity
An identity is an equation that holds true for all values of the variable involved. For example, the equation 2(x + 1) = 2x + 2 is an identity because it simplifies to a true statement regardless of the value of x. Identifying an identity involves showing that both sides of the equation are equivalent for any input.
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Conditional Equation
A conditional equation is an equation that is true only for specific values of the variable. For instance, the equation x + 2 = 5 is conditional because it is only true when x equals 3. Solving a conditional equation typically yields a solution set that includes one or more specific values.
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Contradiction
A contradiction is an equation that has no solution because it leads to a false statement. For example, the equation x + 1 = x - 1 results in 1 = -1, which is impossible. Recognizing a contradiction involves simplifying the equation to a point where it clearly cannot be true for any value of the variable.
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