Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. -0.6(x-5)+0.8(x-6) = 0.2x - 1.8

Key Concepts

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 means recognizing that both sides of the equation are equivalent for every possible input.

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 finite set of solutions, which can be expressed as a solution set.

Contradiction

A contradiction is an equation that has no solutions, meaning there are no values of the variable that can satisfy the equation. An example is the equation x + 1 = x, which simplifies to 1 = 0, a false statement. Recognizing a contradiction is crucial as it indicates that the equation cannot be true under any circumstances.