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8. Using the Distributive Property as a good first step to solving the equation 7(5x + 2) = - 4(6 - 5x)

A. 35x + 14 = -24 - 20x
B. 35x + 2 = 24 - 20x
C. 35x + 2 = -24 - 5x
D. 5x + 14 = 6 + 20x
E. 35x + 14 = -24 + 20x

1 answer

To solve the equation \(7(5x + 2) = -4(6 - 5x)\) using the Distributive Property, we first apply the property to both sides of the equation.

  1. Distributing on the left side: \[ 7(5x) + 7(2) = 35x + 14 \]

  2. Distributing on the right side: \[ -4(6) + (-4)(-5x) = -24 + 20x \]

Now, substituting these results back into the equation gives: \[ 35x + 14 = -24 + 20x \]

Now let's check the answer options:

  • A. \(35x + 14 = -24 - 20x\) (Incorrect)
  • B. \(35x + 2 = 24 - 20x\) (Incorrect)
  • C. \(35x + 2 = -24 - 5x\) (Incorrect)
  • D. \(5x + 14 = 6 + 20x\) (Incorrect)
  • E. \(35x + 14 = -24 + 20x\) (Correct)

Thus, the correct answer is: E. \(35x + 14 = -24 + 20x\).