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Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36.

A 2x + 14 = 36
B (2 • x) + (2 • 7) = 36
C 2x + 7 = 36
D 2(x + 7) = 72
E x + 14 = 36
F x + 7 = 18
Yes No Not Enough Information

2 Answers

3 votes

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.

User Charles Darke
by
7.6k points
5 votes

Answer:

Therefore, the first correct step would be option B,

after that the next step would be option A then option F as shown above;

Remaining options are not enough information to solve the given equation 2(x+7) = 36.

Step-by-step explanation:

User McKabue
by
8.4k points

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