Question
2. 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)ResponsesThere is no way to know if there is a solution to the equation.There is no way to know if there is a solution to the equation.The only solution to the equation is 1The only solution to the equation is 1There are no solutions to the equation.There are no solutions to the equation.The only solution to the equation is -6The only solution to the equation is -6There are infinitely many solutions to the equation.
Answers
GPT-4o mini
Let's examine the equation and the steps given:
1. Start with:
\( 3x - 9x + 1 = 2(-3x + 1) - 1 \)
2. Simplifying the left side:
\( 3x - 9x + 1 = -6x + 1 \)
So this simplifies to:
\( -6x + 1 = -6x + 1 \)
3. Now let's analyze the final equation \( -6x + 1 = -6x + 1 \):
This is an identity; it holds true for all values of \( x \).
Since the equation simplifies down to a true identity, we conclude that:
**There are infinitely many solutions to the equation.**
So the correct response is: **There are infinitely many solutions to the equation.**
1. Start with:
\( 3x - 9x + 1 = 2(-3x + 1) - 1 \)
2. Simplifying the left side:
\( 3x - 9x + 1 = -6x + 1 \)
So this simplifies to:
\( -6x + 1 = -6x + 1 \)
3. Now let's analyze the final equation \( -6x + 1 = -6x + 1 \):
This is an identity; it holds true for all values of \( x \).
Since the equation simplifies down to a true identity, we conclude that:
**There are infinitely many solutions to the equation.**
So the correct response is: **There are infinitely many solutions to the equation.**