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Fill in the blanks to solve the equation 2(3x+1)=4x+3 using the steps listed below.(4 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.2(3x+1)=4x+3Distributive Property: Response areax+2=4x+3Subtract 4x from both sides of the equation: 6x−4x+2=4x−4x+3Combine Like Terms: Response area+2=Response areaSubtract 2 from both sides of the equation: 2x+2−2=3−2Combine Like Terms: 2x=1Divide both sides of the equation by 2: 2x2=12Solution: x=Response areaSkip to navigation

1 answer

To solve the equation \( 2(3x + 1) = 4x + 3 \) using the steps provided, we can fill in the blanks as follows:

  1. Distributive Property:
    \( 2(3x + 1) = 6x + 2 \)
    Therefore, the equation becomes:
    \( 6x + 2 = 4x + 3 \)

  2. Subtract 4x from both sides of the equation:
    \( 6x - 4x + 2 = 4x - 4x + 3 \)
    This simplifies to:
    \( 2x + 2 = 3 \)

  3. Subtract 2 from both sides of the equation:
    \( 2x + 2 - 2 = 3 - 2 \)
    This simplifies to:
    \( 2x = 1 \)

  4. Divide both sides of the equation by 2:
    \( \frac{2x}{2} = \frac{1}{2} \)
    This gives us the solution:
    \( x = \frac{1}{2} \)

Here are the filled response areas:

  1. Distributive Property: 6x + 2
  2. Combine Like Terms: 2x + 2
  3. Combine Like Terms: 3
  4. Solution: \(\frac{1}{2}\)

Let me know if you need further assistance!