Final answer:
The first step in simplifying the equation 8(x + 2) = 4(2x + 9) is to deal with the parentheses by distribution. However, expanding both sides as described leads to 8x canceling out, suggesting no solution, which indicates an error in the initial equation. Proper simplification follows the order of operations and requires a final check to ensure the solution is reasonable.
Step-by-step explanation:
The first step in simplifying the equation 8(x + 2) = 4(2x + 9) is Part A: D) Parentheses. You need to distribute the numbers outside the parentheses to the terms inside the parentheses.
Part B: To solve for x in the equation, first expand both sides:
- 8x + 16 = 8x + 36
- Subtract 8x from both sides: 16 = 36 (which is not possible, suggesting no solution or a potential error in the original equation. In this case, it appears to be a mistake, as the terms 8x should not cancel each other out if we are to find a solution for x.)
Given that the problem seems to contain a mistake, we would either seek clarification on the equation or consider an alternative approach to solving for x if additional information were provided.
Part C: To simplify the equation using order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right), you should start with parentheses by distributing the coefficients to the terms inside. Then combine like terms if any are present, and finally isolate the variable x to solve the equation, ensuring that you always perform operations on both sides of the equation equally to maintain its balance.