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Fill in the blanks to solve the equation 2(3x+1)=4x+3 using the steps listed below.(4 points)

2(3x+1)=4x+3
Distributive Property: ?x+2=4x+3
Subtract 4x from both sides of the equation: 6x−4x+2=4x−4x+3
Combine Like Terms: ?+2=?
Subtract 2 from both sides of the equation: 2x+2−2=3−2
Combine Like Terms: 2x=1
Divide both sides of the equation by 2: 2x/2=1/2
Solution: x=?
Responses: −2x 1/2 5 3 −1/2 6 2x 10x −3

1 answer

Let's fill in the blanks step by step to solve the equation \( 2(3x+1)=4x+3 \).

  1. Start with the original equation: \[ 2(3x+1) = 4x + 3 \]

  2. Apply the Distributive Property: \[ 6x + 2 = 4x + 3 \] (This means we replace the first blank with "6x")

  3. Subtract \( 4x \) from both sides of the equation: \[ 6x - 4x + 2 = 4x - 4x + 3 \] (In this case, the second blank corresponds to "6x", as we already did it above)

  4. Combine Like Terms: \[ 2x + 2 = 3 \] (This means we fill the third blank with "2x")

  5. Subtract 2 from both sides of the equation: \[ 2x + 2 - 2 = 3 - 2 \] (We have already established that \( 2x \) on the left remains as is, so the left side is correctly represented)

  6. Combine Like Terms: \[ 2x = 1 \] (This means the final part of the equation is already shown and we leave it as it is)

  7. Divide both sides of the equation by 2: \[ \frac{2x}{2} = \frac{1}{2} \] (In this case, "x = 1/2" is our concluding statement)

Thus, to complete the response with the blanks filled in, we have:

  1. For the first blank: 6x
  2. For the second blank: 2x
  3. For the third blank: 1/2 (solution)

So the final output based on the given instructions would be:

  1. Distributive Property: 6x + 2 = 4x + 3
  2. Combine Like Terms: 2x + 2 = 3
  3. Solution: 1/2