Look at the steps for solving the equation and choose a true statement.
3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1
(1 point)
Responses
There are no solutions to the equation.
There are no solutions to the equation.
The only solution to the equation is 1
The only solution to the equation is 1
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is -6
The only solution to the equation is -6
There is no way to know if there is a solution to the equation.
The only solution to the equation is -6
To determine if the given equation has a solution, we need to simplify both sides of the equation and see if they are equivalent.
Starting with the given equation: 3x - 9x + 1 = 2(-3x + 1) - 1
First, let's simplify both sides separately.
On the left side, we combine like terms: -6x + 1
On the right side, we apply the distributive property: 2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1
Now we have the simplified equation: -6x + 1 = -6x + 1
Comparing the simplified equation, we can see that both sides are equal. Therefore, the true statement is:
The only solution to the equation is -6.
So, the correct answer is: The only solution to the equation is -6.