Let's analyze and solve the equation step by step to clarify the student's work.
The original equation given is:
Now let's simplify both sides.
-
Distribute on both sides:
Which gives: -
Next, we isolate the terms involving
by subtracting from both sides:
At this point, we notice that we have reached a contradiction. The simplified form
The conclusion would be:
- The student made an error in determining the solutions. The properly analyzed equation shows that there are no solutions, indicating that the equation is inconsistent.
In conclusion, based on the correct simplification:
- The equation
does not have infinitely many solutions; it has no solutions.