Solve for x 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 one solution: x=0.
The equation has one solution: x equals 0 .
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 .
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To solve for x, we can start by distributing the 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Next, we can simplify the equation:
12x + 0 = 12x
Since the x term is the same on both sides of the equation, it cancels out:
0 = 0
The equation has infinite solutions, since any value of x will satisfy the equation.
To solve the equation 6(2x+4)−24=12x, we begin by distributing the 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Next, we combine like terms:
12x = 12x
At this point, we can see that the variables have cancelled out and all we are left with is 0 = 0.
Since the equation is true for any value of x, the equation has infinite solutions.
Therefore, the correct response is: The equation has infinite solutions.
To determine if the equation has one, none, or infinite solutions, we need to solve for x and simplify the equation.
Let's start by distributing the 6 to both terms inside the parentheses:
12x + 24 - 24 = 12x
Now simplify by combining like terms:
12x + 0 = 12x
Notice that the variable x appears on both sides of the equation, and there are no constants left. This means that the equation has infinite solutions.
Explanation:
To solve the equation, we first distributed the 6 to both terms inside the parentheses. This gives us 12x + 24 - 24 = 12x. Then, by combining like terms, we simplify the equation to 12x + 0 = 12x. Since the variable x appears on both sides and there are no constants left, this indicates that the equation has infinite solutions, as any value of x will satisfy the equation.