Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 2(x-8) = 3x-16

An identity is an equation that holds true for all values of the variable involved. For example, the equation 2(x) = 2x is an identity because it is valid for any value of x. In solving equations, if both sides simplify to the same expression regardless of the variable's value, the equation is classified as an identity.

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. When solving such equations, the solution set consists of the values that satisfy the equation.

A contradiction is an equation that has no solution because it is never true for any value of the variable. An example is the equation x + 1 = x, which simplifies to 1 = 0, a false statement. In this case, the solution set is empty, indicating that there are no values that can satisfy the equation.