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Solve for x to determine if the equation has one, none, or infinite solutions.
6(2x + 4) - 24 = 12x
A. The equation has infinite solutions.
B. The equation has one solution: x = -20.
C. The equation has one solution: x = 0.
D. The equation has no solution.
6(2x + 4) - 24 = 12x
A. The equation has infinite solutions.
B. The equation has one solution: x = -20.
C. The equation has one solution: x = 0.
D. The equation has no solution.
Answers
Answered by
GPT-4o mini
To solve the equation \( 6(2x + 4) - 24 = 12x \), we start by simplifying and rearranging the left side.
1. Distribute \( 6 \) to both terms inside the parentheses:
\[
6 \cdot 2x + 6 \cdot 4 = 12x + 24
\]
Substituting back into the equation gives:
\[
12x + 24 - 24 = 12x
\]
2. Now simplify the left side:
\[
12x + 24 - 24 = 12x
\]
which simplifies to:
\[
12x = 12x
\]
3. This results in an identity, meaning that the equation is true for all values of \( x \).
Since the equation simplifies to \( 12x = 12x \), we conclude that the equation has infinite solutions.
Therefore, the correct answer is:
A. The equation has infinite solutions.
1. Distribute \( 6 \) to both terms inside the parentheses:
\[
6 \cdot 2x + 6 \cdot 4 = 12x + 24
\]
Substituting back into the equation gives:
\[
12x + 24 - 24 = 12x
\]
2. Now simplify the left side:
\[
12x + 24 - 24 = 12x
\]
which simplifies to:
\[
12x = 12x
\]
3. This results in an identity, meaning that the equation is true for all values of \( x \).
Since the equation simplifies to \( 12x = 12x \), we conclude that the equation has infinite solutions.
Therefore, the correct answer is:
A. The equation has infinite solutions.
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