Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3.
The equation has one solution: x equals 3 .
The equation has one solution: x=−3.
1 answer
Let's solve the equation \( 3(x+2) - 6 = 3x \).
Distribute the \( 3 \) on the left side: \[ 3x + 6 - 6 = 3x \]
Simplify the left side: \[ 3x = 3x \]
This results in the equation \( 3x = 3x \), which is true for all values of \( x \).
Since both sides of the equation are identical, this means that the equation has infinite solutions.
Thus, the correct response is: The equation has infinite solutions.
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1 answer
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