Question

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

Answer 1

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

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

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

Now we can set these two results equal to each other:
\[
35x + 14 = -24 + 20x
\]

Therefore, the simplified equation is:
\[
35x + 14 = -24 + 20x
\]

The correct choice is:
**A. 35x + 14 = -24 + 20x**

Answer 2

are you sure this is correct

Answer 3

Let's recheck the equation step by step to ensure we apply the Distributive Property correctly.

Given the equation:
\[
7(5x + 2) = -4(6 - 5x)
\]

**Step 1: Distributing on the left side**
\[
7 \cdot 5x + 7 \cdot 2 = 35x + 14
\]

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

So after distributing, we have:
\[
35x + 14 = -24 + 20x
\]

Now, let's revisit the choices you provided:

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

B. \( 5x + 14 = 6 + 20x \)

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

D. \( 35x + 2 = -24 - 5x \)

E. \( 35x + 2 = 24 - 20x \)

After verifying, I confirm that my previous response remains accurate. The correct simplification from the original equation is indeed:
\[
35x + 14 = -24 + 20x
\]

So the answer is **A. 35x + 14 = -24 + 20x**. Thank you for your patience, and I appreciate your diligence in confirming the solution!