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Correct the equation [tex]\(2x + 4 = 4x - 2\)[/tex]. Select the reason that correctly solves for [tex]\(x\)[/tex].

A. Add 2, subtract [tex]\(4x\)[/tex], then divide by -2.
B. Subtract 4, subtract [tex]\(2x\)[/tex], then divide by -2.
C. Subtract 4, subtract [tex]\(2x\)[/tex], then divide by 2.
D. Add 2, subtract [tex]\(2x\)[/tex], then divide by 2.



Answer :

GinnyAnswer
To solve the equation [tex]\(2x + 4 = 4x - 2\)[/tex], we will follow a series of logical mathematical steps to isolate [tex]\(x\)[/tex]. Here's the step-by-step solution:

1. Add 2 to both sides of the equation:

Given equation:
[tex]\[ 2x + 4 = 4x - 2 \][/tex]

Adding 2 to both sides:
[tex]\[ 2x + 4 + 2 = 4x - 2 + 2 \][/tex]

Simplifying this, we get:
[tex]\[ 2x + 6 = 4x \][/tex]

2. Subtract [tex]\(2x\)[/tex] from both sides:

[tex]\[ 2x + 6 - 2x = 4x - 2x \][/tex]

Simplifying this, we get:
[tex]\[ 6 = 2x \][/tex]

3. Divide by 2:

[tex]\[ \frac{6}{2} = \frac{2x}{2} \][/tex]

Simplifying this, we get:
[tex]\[ 3 = x \][/tex]

Therefore, the correct value of [tex]\(x\)[/tex] is 3.

The correct reasoning to solve for [tex]\(x\)[/tex] in this equation is:
Add 2, subtract [tex]\(2x\)[/tex], then divide by 2.

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