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
translate the number stuff
Translate the number "stuff" into which language? Please specify the language you would like the translation to be in.
can you make the explanation seem lazier?
Sure, here's a lazy explanation:
So, we've got this equation thingy, y = x - ab , and we need to find 'a'. Now, let's see what these students did.
Student 1 was all like y = (x-a)/b. Then they were like, "Okay, let's get 'a' by itself." They wrote stuff like by = x - a, but they made a mistake, 'cause they should've multiplied by b, not divided by b. So, their answer is wrong.
Student 2 was like y = (x-a)/b. Then they tried to isolate 'a' and did some math. They got to the point where it was y/(b-x) = -a. But they messed up, it should've been -y/b = a. So, their answer is also wrong.
Student 3 was like y = (x-a)/b. Then they did some math and got by - x = -a. They rearranged and boom! They got a = -by + x. So, their answer is correct.
There you go, Student 3 is the lazy winner who solved the equation correctly. The other two students just made messed up calculations.