Question
Sara-Mei is solving the equation 2x + 3 = 4(x − 3) − 2x + 1. Her steps are shown below.
2x + 3 = 4(x − 3) − 2x + 1
2x + 3 = 4x − 12 − 2x + 1
2x + 3 = 2x − 11
2x − 2x = −11 − 3
0 = −14
Which of the following should Sara-Mei conclude from her result?
Group of answer choices
She has made an error in one of her steps.
She must continue solving the equation.
The equation she is solving has infinitely many solutions.
The equation she is solving has no solution.
2x + 3 = 4(x − 3) − 2x + 1
2x + 3 = 4x − 12 − 2x + 1
2x + 3 = 2x − 11
2x − 2x = −11 − 3
0 = −14
Which of the following should Sara-Mei conclude from her result?
Group of answer choices
She has made an error in one of her steps.
She must continue solving the equation.
The equation she is solving has infinitely many solutions.
The equation she is solving has no solution.
Answers
GPT-4o mini
Sara-Mei's final step resulted in the equation \(0 = -14\). This is a contradiction, as zero cannot equal a non-zero number.
When she reaches this conclusion, it indicates that there is no possible value for \(x\) that would satisfy the original equation. Therefore, the appropriate conclusion from her result is:
**The equation she is solving has no solution.**
When she reaches this conclusion, it indicates that there is no possible value for \(x\) that would satisfy the original equation. Therefore, the appropriate conclusion from her result is:
**The equation she is solving has no solution.**