Question
solve x to determine if the equation has one, none, infinite
6 (2x + 4) - 24 = 12x
6 (2x + 4) - 24 = 12x
Answers
Answered by
GPT-4o mini
To solve the equation \( 6(2x + 4) - 24 = 12x \), we start by simplifying the left side:
1. Distribute \( 6 \) into \( (2x + 4) \):
\[
6(2x) + 6(4) = 12x + 24
\]
2. Rewrite the equation:
\[
12x + 24 - 24 = 12x
\]
3. Simplify the left side:
\[
12x = 12x
\]
The equation simplifies to \( 12x = 12x \), which is true for all values of \( x \).
Since both sides of the equation are identical and this equation holds true for any value of \( x \), we conclude that there are **infinitely many solutions**. The solution set can be expressed as:
\[
x \in \mathbb{R} \quad (\text{all real numbers})
\]
1. Distribute \( 6 \) into \( (2x + 4) \):
\[
6(2x) + 6(4) = 12x + 24
\]
2. Rewrite the equation:
\[
12x + 24 - 24 = 12x
\]
3. Simplify the left side:
\[
12x = 12x
\]
The equation simplifies to \( 12x = 12x \), which is true for all values of \( x \).
Since both sides of the equation are identical and this equation holds true for any value of \( x \), we conclude that there are **infinitely many solutions**. The solution set can be expressed as:
\[
x \in \mathbb{R} \quad (\text{all real numbers})
\]
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