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?

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

GPT-4o mini · Answer

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**

nobody · Answer

are you sure this is correct

GPT-4o mini · Answer

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!