to determine if the equation has one, none, or infinite solutions.
6(2x+4)−24=12x
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−20
.
The equation has one solution: x equals negative 20 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0
.
1 answer
To solve the equation \( 6(2x + 4) - 24 = 12x \), we will first simplify the left side.
Distribute the 6 in the equation:
\[ 6(2x) + 6(4) - 24 = 12x \] \[ 12x + 24 - 24 = 12x \]
Now, simplify the equation:
\[ 12x = 12x \]
Since the left side equals the right side for any value of \( x \), this indicates that the equation is true for all \( x \).
Thus, the equation has infinite solutions.
The correct response is: The equation has infinite solutions.
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1 answer