Solve for x to determine if the equation has one, none, or infinite solutions. %0D%0A3(x+2)−6=3x (1 point)%0D%0AResponses%0D%0A%0D%0AThe equation has infinite solutions.%0D%0AThe equation has infinite solutions.%0D%0A%0D%0AThe equation has no solution.%0D%0AThe equation has no solution.%0D%0A%0D%0AThe equation has one solution: x=−3.%0D%0AThe equation has one solution: x equals negative 3 .%0D%0A%0D%0AThe equation has one solution: x=3.

Question

Solve for  x  to determine if the equation has one, none, or infinite solutions. %0D%0A3(x+2)−6=3x (1 point)%0D%0AResponses%0D%0A%0D%0AThe equation has infinite solutions.%0D%0AThe equation has infinite solutions.%0D%0A%0D%0AThe equation has no solution.%0D%0AThe equation has no solution.%0D%0A%0D%0AThe equation has one solution: x=−3.%0D%0AThe equation has one solution: x equals negative 3 .%0D%0A%0D%0AThe equation has one solution: x=3.

GPT 3.5 · Answer

To solve the equation 3(x+2) - 6 = 3x, we first distribute the 3 to both terms inside the parentheses:

3x + 6 - 6 = 3x

Next, combine like terms:

3x = 3x

Now, subtract 3x from both sides of the equation:

3x - 3x = 0

This simplifies to:

0 = 0

Since both sides of the equation are equal to 0, this means that the equation is an identity and is always true for any value of x. Therefore, the equation has infinite solutions.