In order to solve for the variable in the equation 2 (4 x + 3) + 4 = 3 x minus (2 x + 4), Giovanni first applies the distributive property. Which equation is a result of this step?

Question

8 x + 3 + 4 = 3 x minus 2 x + 4
8 x + 6 + 4 = 3 x minus 2 x minus 4
6 x + 5 + 4 = 3 x minus x + 3
6 x + 3 + 4 = 3 x minus x + 4

Answer 1

To apply the distributive property to the equation \(2(4x + 3) + 4 = 3x - (2x + 4)\), we need to first distribute \(2\) on the left side and distribute \(-1\) (or negate) on the right side.

1. Left Side:
   \(2(4x + 3) = 2 \cdot 4x + 2 \cdot 3 = 8x + 6\)
   Thus, the left side becomes:
   \(8x + 6 + 4\)

2. Right Side:
   The expression \(3x - (2x + 4)\) can be rewritten by distributing \(-1\):
   \(3x - 2x - 4\)
   Thus, the right side becomes:
   \(3x - 2x - 4 = x - 4\)

Combining both sides, we have:

Left Side:
\(8x + 6 + 4\) simplifies to \(8x + 10\)

Right Side:
\(x - 4\)

So the equation after applying the distributive property is:
\[ 8x + 10 = x - 4 \]

Now we compare this with the equations provided:

1. \(8x + 3 + 4 = 3x - 2x + 4\)
2. \(8x + 6 + 4 = 3x - 2x - 4\)
3. \(6x + 5 + 4 = 3x - x + 3\)
4. \(6x + 3 + 4 = 3x - x + 4\)

The correct result from applying the distributive property is:

Answer: The first equation, \(8x + 6 + 4 = 3x - 2x - 4\) (after calculation, we see that \(3x - 2x = x\) and this expression still equals \(x - 4\) confirming our distribution).

Therefore, the answer is: \(8x + 6 + 4 = 3x - 2x - 4\).