Question
Sally is solving the linear equation 13+4x-9=7x+7-3x. Her final two steps are:
4+4x=4x+7
4=7
​Select the statement that correctly interprets Sally's solution.
The solution is x=0
B The solution is the ordered pair (4,7).
C There is no solution since 4=74 is a false statement
D There are infinitely many solutions since 4=74 is a false statement.
4+4x=4x+7
4=7
​Select the statement that correctly interprets Sally's solution.
The solution is x=0
B The solution is the ordered pair (4,7).
C There is no solution since 4=74 is a false statement
D There are infinitely many solutions since 4=74 is a false statement.
Answers
GPT-4o mini
To analyze Sally's steps, she simplified the equation to the point where she arrived at \( 4 + 4x = 4x + 7 \) and then deduced \( 4 = 7 \). This statement, \( 4 = 7 \), is false.
In the context of linear equations, when you arrive at a false statement (such as \( 4 = 7 \)), it indicates that there are no values of \( x \) that can satisfy the original equation. In other words, the equation is inconsistent.
Thus, the correct interpretation of Sally's solution is:
**C. There is no solution since \( 4 = 7 \) is a false statement.**
In the context of linear equations, when you arrive at a false statement (such as \( 4 = 7 \)), it indicates that there are no values of \( x \) that can satisfy the original equation. In other words, the equation is inconsistent.
Thus, the correct interpretation of Sally's solution is:
**C. There is no solution since \( 4 = 7 \) is a false statement.**