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

A. [tex]\(8x + 3 + 4 = 3x - 2x + 4\)[/tex]
B. [tex]\(8x + 6 + 4 = 3x - 2x - 4\)[/tex]
C. [tex]\(6x + 5 + 4 = 3x - x + 3\)[/tex]
D. [tex]\(6x + 3 + 4 = 3x - x + 4\)[/tex]

Sagot :

GinnyAnsweridn
To solve the equation [tex]\(2(4x + 3) + 4 = 3x - (2x + 4)\)[/tex], Giovanni first applies the distributive property. Let’s do this step-by-step.

### Step 1: Apply the distributive property

Left Side: [tex]\(2(4x + 3) + 4\)[/tex]
- Multiply [tex]\(2\)[/tex] with both terms inside the parentheses.
[tex]\[2 \cdot 4x + 2 \cdot 3 = 8x + 6\][/tex]
- Now, add the [tex]\(+4\)[/tex] outside the parentheses to the result.
[tex]\[8x + 6 + 4\][/tex]

Right Side: [tex]\(3x - (2x + 4)\)[/tex]
- Distribute the negative sign to both terms inside the parentheses.
[tex]\[3x - 2x - 4\][/tex]

### Step 2: Write the combined equation
Now combine both simplified sides:
[tex]\[8x + 6 + 4 = 3x - 2x - 4\][/tex]

So, the equation resulting from applying the distributive property to both sides is:
[tex]\[8x + 6 + 4 = 3x - 2x - 4\][/tex]

Therefore, the correct equation as a result of applying the distributive property is:
[tex]\[8x + 6 + 4 = 3x - 2x - 4\][/tex]

So, the correct answer is:
[tex]\[8x + 6 + 4 = 3x - 2x - 4\][/tex]
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