Let's analyze the equation you provided to determine how many solutions there are.
You started with the equation:
\[ 6x - 6 = 4x - 2 \]
You then isolated \( x \) and found:
\[ 2x - 6 = -2 \]
Next, you solved for \( x \):
\[ 2x = 4 \]
\[ x = 2 \]
This means you found one solution, which is \( x = 2 \).
To check if there might be more solutions or if it might be a special case (like no solutions or infinitely many), we can set the original equation into a simpler form. After isolating \( x \), we can confirm whether this solution is valid.
By substituting \( x = 2 \) back into the original equation:
Left-hand side: \[ 6(2) - 6 = 12 - 6 = 6 \]
Right-hand side: \[ 4(2) - 2 = 8 - 2 = 6 \]
Both sides are equal, confirming that the solution \( x = 2 \) satisfies the original equation.
Since we reach the same point from both sides and find one unique solution for \( x \), we conclude:
The equation has one solution.
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