Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses
The equation has one solution: x=3.
The equation has one solution: , x equals 3, .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: , x equals negative 3, .
The equation has infinite solutions.
The equation has infinite solutions.
Subtract 3x from both sides of the equation:
3(x+2)-6 = 3x
3x+6-6 = 3x
3x = 3x
The variable has canceled out on both sides and what remains is a true statement. This means that the equation has infinite solutions, as any value of x will satisfy the equation. Therefore, the correct answer is:
The equation has infinite solutions.