Final answer:
The missing reason in the given sequence of algebra solving steps is the Division Property of Equality, which is applied to solve for x, giving x = -18.
Step-by-step explanation:
The student is asking for the missing reason in a sequence of steps to solve an algebraic equation. The sequence shows the application of various properties to bring the equation from its original form to the solution for x. After isolating the term 2x on one side of the equation and obtaining 2x = -36, the next logical step is dividing both sides by 2 to solve for x. The rule that applies to this step is the Division Property of Equality, which states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. Thus, when 2x = -36 is divided by 2, it simplifies to x = -18.