Question

Students were asked to solve the equation y = (x - a)/b 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; - b * y + x = a

Which student solved the equation correctly? Justify your answer by explaining why the other two students solved the equation incorrectly.

Answer 1

Student 3 solved the equation correctly.

Student 1 made a mistake in the last step by subtracting "x" from both sides of the equation instead of adding it to both sides. This mistake resulted in a sign error in the final answer.

Student 2 also made a sign error in the last step by subtracting "a" from both sides of the equation with a negative sign, instead of adding it. This mistake also resulted in a sign error in the final answer.

Student 3 correctly subtracted "x" from both sides of the equation in the second step and then multiplied both sides by "-b" to isolate "a". This resulted in the correct expression for "a" on the right side of the equation. Therefore, Student 3 solved the equation correctly.