to determine if the equation has one, none, or infinite solutions.
6(2x+4)−24=12x
(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=0
.
The equation has one solution: x equals 0 .
The equation has one solution: x=−20
.
1 answer
To solve the equation \(6(2x + 4) - 24 = 12x\), let's first simplify the left side.
Distribute the 6: \[ 12x + 24 - 24 = 12x \]
This simplifies to: \[ 12x = 12x \]
Now, subtract \(12x\) from both sides: \[ 12x - 12x = 12x - 12x \implies 0 = 0 \]
Since the equation simplifies to \(0 = 0\), which is always true, it means that there are an infinite number of solutions.
Therefore, the correct response is: The equation has infinite solutions.
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