Final answer:
The options A and B are the correct first steps for solving the linear equation 2(x + 7) = 36, both involving the correct application of the distributive property. Other options do not correctly apply the distributive property or incorrectly alter the original equation.
Step-by-step explanation:
The question involves solving the linear equation 2(x + 7) = 36. To determine which steps could correctly represent the first step in solving this equation, we must evaluate the options provided.
- A. 2x + 14 = 36: Yes. This option represents the correct application of the distributive property to the left side of the equation.
- B. (2 • x) + (2 • 7) = 36: Yes. This is another form of the distributive property applied correctly, although it has not been simplified by carrying out the multiplications.
- C. 2x + 7 = 36: No. This incorrectly applies the distributive property as it does not multiply the 7 by 2.
- D. 2(x + 7) = 72: No. This represents a change in the original equation, doubling the right-hand side without a proper basis.
- E. x + 14 = 36: No. This equation does not include the multiplication by 2, which is essential to match the left side of the original equation.
- F. x + 7 = 18: No. This simplifies the equation too far by dividing both sides by 2 without justification.
Always eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable, aligning with good practices in problem solving.