Follow these steps in order on the algebraic expression: (1) Add 5y to 2x, (2) multiply the resulting sum by 3, and (3) subtract x + y from the product. What is the simplified final expression?

Introduction / Context:This question tests procedural algebra skills: building an expression step by step according to instructions and then simplifying. It simulates how algebraic expressions can model multi step operations.

Given Data / Assumptions:

• We start with variables x and y.
• Step 1: Add 5y to 2x.
• Step 2: Multiply this sum by 3.
• Step 3: Subtract x + y from the product.
• We must simplify the resulting expression.

Concept / Approach:We carefully carry out the operations in the specified order and then combine like terms. Each step transforms the expression into a new one. Keeping track of the current expression after each step is crucial to avoid confusion.

Step-by-Step Solution:Step 1: Add 5y to 2x. The result is 2x + 5y.Step 2: Multiply the result by 3. We get 3 * (2x + 5y) = 6x + 15y.Step 3: Subtract x + y from this product. So the new expression is (6x + 15y) - (x + y).Step 4: Distribute the minus sign: (6x + 15y) - x - y = 6x - x + 15y - y.Step 5: Combine like terms: 6x - x = 5x and 15y - y = 14y.Step 6: The final simplified expression is 5x + 14y.

Verification / Alternative check:You can test the expression by substituting specific values for x and y, for example x = 1, y = 2, and comparing the result of performing the steps numerically with the value given by 5x + 14y. Both approaches should give the same number.

Why Other Options Are Wrong:5x + 16y suggests that 15y - y was incorrectly computed as 16y instead of 14y.5x + 5y ignores part of the y contribution from the multiplication step.\"None\" is incorrect because a valid simplified expression clearly exists.

Common Pitfalls:Forgetting to distribute the minus sign over both x and y in the expression (x + y).Mixing the order of steps, such as subtracting before multiplying by 3.Careful adherence to the step order and neat algebraic manipulation prevent such mistakes.

Final Answer:The final simplified expression is 5x + 14y.