An equation is a statement that two expressions are equal and can be solved to find a value for the variable. On the other hand, an identity is a statement that is true for all values of the variable.
In the equation 2(x + 3) = 10, the goal is to find a value of x that makes the equation true. By simplifying the left-hand side of the equation, we get 2x + 6 = 10, and then by subtracting 6 from both sides, we get 2x = 4, and finally, by dividing both sides by 2, we get x = 2. So the solution to the equation is x = 2.
In the identity 2(x + 3) = 2x + 6, the left-hand side and right-hand side are already equal for all values of x. There is no need to solve for x, as the statement is true regardless of what value x takes.