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

To simplify the equation \( 7(5x + 2) = -4(6 - 5x) \) using the Distributive Property, we need to distribute the \( 7 \) on the left side and the \( -4 \) on the right side.

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

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

Now we can write the equation with the simplified expressions:
\[
35x + 14 = -24 + 20x
\]

This is the simplified equation after applying the Distributive Property.