to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x
(1 point)
Responses
The equation has one solution: x=−3
.
The equation has one solution: x equals negative 3 .
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
1 answer
To solve the equation \( 3(x+2) - 6 = 3x \), let's follow these steps:
Distribute the \( 3 \) on the left side: \[ 3x + 6 - 6 = 3x \]
Simplify the left side: \[ 3x = 3x \]
At this point, we see that both sides of the equation are identical. This means that any value for \( x \) would satisfy the equation.
Since the equation simplifies to a true statement, we conclude that:
The equation has infinite solutions.
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