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

Question

, you could simplify this equation to get which of these choices?(1 point)
Responses

A.35x+2=24−20x

B.35x+14=−24−20x

C.35x+14=−24+20x

D.5x+14=6+20x

E.35x+2=−24−5x

Answer 1

To solve the equation \( 7(5x + 2) = -4(6 - 5x) \) using the Distributive Property, we will first distribute the constants on both sides of the equation.

Starting with the left side: \[ 7(5x + 2) = 7 \cdot 5x + 7 \cdot 2 = 35x + 14. \]

Now, for the right side: \[ -4(6 - 5x) = -4 \cdot 6 + (-4) \cdot (-5x) = -24 + 20x. \]

Putting it all together, we get: \[ 35x + 14 = -24 + 20x. \]

Looking at the response options, this matches choice C:

C. \( 35x + 14 = -24 + 20x \).

So the correct answer is C.