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

you could simplify this equation to get which of these choices?

1 answer

To simplify the equation \( 7(5x + 2) = -4(6 - 5x) \) using the Distributive Property, you would first distribute the numbers outside the parentheses.

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

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

Now we can rewrite the equation with the distributed values: \[ 35x + 14 = -24 + 20x \]

So the simplified equation you arrive at is: \[ 35x + 14 = -24 + 20x \]

You could use this form to solve for \( x \).