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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

options:

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 this equation.
There is no way to know if there is a solution to this equation.

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.

1 answer

Let's analyze the steps you provided for solving the equation:

  1. Starting equation: \(3x - 9x + 1 = 2(-3x + 1) - 1\).
  2. Simplifying the left side: \(3x - 9x + 1 = -6x + 1\).
  3. Simplifying 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 (-6x + 1 = -6x + 1), this means that the equation holds true for all values of \(x\).

Thus, the correct statement is: There are infinitely many solutions to the equation.