Solve for x to determine if the equation has one, none, or infinite solutions
6 (2x + 4) - 24 = 12x
A) the equation has one solution: x = 0
B) the equation has one solution: x = -20
C) the equation has infinite solutions.
D) the equation has no solutions
To solve for x, first simplify the left side of the equation:
6(2x + 4) - 24 = 12x
By multiplying 6 with both terms inside the parentheses, we get:
12x + 24 - 24 = 12x
Next, we can combine like terms:
12x + 0 = 12x
Now, subtract 12x from both sides of the equation:
0 = 0
The equation simplifies to 0 = 0, which is always true. This means that for any value of x, the equation holds true. Therefore, the equation has infinite solutions.
Therefore, the correct answer is:
C) the equation has infinite solutions.