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 one solution: x=−20.
The equation has one solution: x equals negative 20 .
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has one solution: x = 0.
To determine if the equation has one, none, or infinite solutions, we can solve it step-by-step.
Given equation: 6(2x+4) - 24 = 12x
Step 1: Distribute 6 to the terms inside the parentheses.
12x + 24 - 24 = 12x
Step 2: Simplify the equation.
12x = 12x
Step 3: Subtract 12x from both sides of the equation.
12x - 12x = 12x - 12x
0 = 0
Step 4: Analyze the result.
Since 0 = 0, this means that the equation is always true, regardless of the value of x. Therefore, the equation has infinite solutions.
The equation has infinite solutions.