Final answer:
The solution of the equation 5x + 15 = 0 involves using the Subtraction and Division Properties of Equality, simplifying to 5x = -15 and then x = -3, and checking that the solution is reasonable by substituting back into the original equation.
Step-by-step explanation:
To justify each step in the solution of the equation 5x + 15 = 0, we apply mathematical operations and properties to isolate the variable x. The goal is to solve for x by getting it by itself on one side of the equation.
- First, apply the Subtraction Property of Equality to both sides to cancel out the constant term, obtaining 5x = -15.
- Next, use the Division Property of Equality by dividing both sides by 5, resulting in x = -3.
- Finally, check the solution by substituting x into the original equation to ensure that the left-hand side equals the right-hand side. If this holds true, the solution is reasonable.
These methods streamline the problem-solving process and ensure the solution we get for x is accurate and reasonable, maintaining consistency with the foundational principles of algebra.