Students were asked to solve the equation y=x−ab for a. Their work is shown below.
Student 1:
y=x−a/b
by=x−a
by−x=a
Student 2:
y=x−a/b
y/b=x−a
y/b−x=−a
−y/b+x=a
Student 3:
y=x−a/b
by=x−a
by−x=−a
−by+x=a
Which student solved the equation correctly? Justify your answer by explaining why the other two students solved the equation incorrectly.
Student 2 solved the equation correctly. The other two students, Student 1 and Student 3, made mistakes in their calculations.
Student 1 incorrectly wrote the equation as y = x - a/b. To isolate a, they should have multiplied both sides by b, not divided by b. So, the correct equation should be by = x - a, not y = x - a/b. When they subtracted x from both sides, they should have subtracted it from x, not from a. Therefore, Student 1's calculation is incorrect.
Student 3 also made a mistake in their calculation. They incorrectly wrote the equation as by = x - a/b. To solve for a, they should have divided x by b, not multiplied by b. So, the correct equation should be by - x = -a, not by - x = a. Therefore, Student 3's calculation is also incorrect.
Only Student 2 correctly rearranged the equation and isolated a on one side to obtain a = -y/b + x. Therefore, Student 2 solved the equation correctly.
Students were asked to solve the equation y=x−ab for a. Their work is shown below.
Student 1:
y=\frac{x-a}{b}
by=x−a
by−x=a
Student 2:
y=\frac{x-a}{b}
y/b=x−a
\frac{y}{b-x}=-a
-\frac{y}{b+x}=a
Student 3:
y=\frac{x-a}{b}
by=x−a
by−x=−a
−by+x=a
Which student solved the equation correctly? Justify your answer by explaining why the other two students solved the equation incorrectly.
Student 3 solved the equation correctly. The other two students, Student 1 and Student 2, made mistakes in their calculations.
Student 1 wrote the equation as y = \frac{x-a}{b}. However, they made an error when isolating 'a'. They wrote by = x - a, but it should actually be by - x = -a. So their equation is incorrect.
Student 2 also made a mistake in their calculation. They wrote the equation as y/b = x - a, which is correct. However, they made an error when isolating 'a'. Instead of \frac{y}{b-x} = -a, it should be -\frac{y}{b} = a. So their equation is incorrect.
Student 3, however, correctly wrote the equation as by - x = -a. They isolated 'a' on one side and obtained the correct equation of a = -by + x. Therefore, Student 3 solved the equation correctly.
translate
translatare
please
Translate
do it
I apologize for the confusion. Here is the translation:
traduce