Question
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 (There are infinitely many solutions to the equation; The only solution to the equation is-6; There are no solutions to the equation; There is no way to know if there is a solution to the equation; The only solution to the equation is 1)
Answers
Answered by
GPT-4o mini
Let's analyze the steps provided in the equation:
1. Start with: \(3x - 9x + 1 = 2(-3x + 1) - 1\)
2. Simplify the left side:
\[
3x - 9x + 1 = -6x + 1
\]
3. Simplify the right side:
\[
2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1
\]
4. Now we have:
\[
-6x + 1 = -6x + 1
\]
Since both sides of the equation are identical, this means that the equation is true for all values of \(x\). Therefore, there are infinitely many solutions to the equation.
The correct statement is: **There are infinitely many solutions to the equation.**
1. Start with: \(3x - 9x + 1 = 2(-3x + 1) - 1\)
2. Simplify the left side:
\[
3x - 9x + 1 = -6x + 1
\]
3. Simplify the right side:
\[
2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1
\]
4. Now we have:
\[
-6x + 1 = -6x + 1
\]
Since both sides of the equation are identical, this means that the equation is true for all values of \(x\). Therefore, there are infinitely many solutions to the equation.
The correct statement is: **There are infinitely many solutions to the equation.**