Students were asked to solve the equation for m. Their work is shown below. Which student solved the equation correctly? Why did the other 2 students solve the equation incorrectly?
3+n divided by m equals b
Without seeing the work of the students, it is not possible to determine which student solved the equation correctly and why the other two students solved it incorrectly. Please provide more information or the work of the students to further analyze and determine the correct solution.
To determine which student solved the equation correctly, we need to analyze their work. However, as you haven't provided the work done by each student, I can only provide general explanations of how the equation could be solved correctly or incorrectly.
The equation 3 + n / m = b is a linear equation in terms of m. To solve it correctly, students need to isolate m on one side of the equation.
Correct solution:
To isolate m, the correct approach would involve subtracting 3 from both sides of the equation. Then, the equation becomes n / m = b - 3. Next, multiplying both sides by m would give n = m(b - 3). Finally, dividing both sides by (b - 3) would give the solution m = n / (b - 3). This student solved the equation correctly by performing the appropriate operations in the correct order.
Incorrect solutions:
1. If a student added 3 to both sides instead of subtracting 3, the equation would become 3 + n / m + 3 = b + 3. This is incorrect because adding 3 to only one side of the equation would change the equation's meaning, resulting in an incorrect solution for m.
2. If a student multiplied both sides by m instead of dividing, the equation would become m(3 + n / m) = m(b). This is also incorrect because multiplying both sides by m doesn't eliminate the m in the denominator on the left side of the equation. The student failed to properly isolate m.
3. If a student attempted to multiply m by (3 + n / m) without distributing correctly, it would result in m * 3 + n = mb. This is incorrect because the student didn't correctly distribute the m on the left side of the equation, leading to an inaccurate solution.
Therefore, the student who solved the equation correctly would be the one who followed the appropriate steps to isolate m on one side of the equation.
To determine which student solved the equation correctly, we need to examine the work of each student. Let's go through the process step by step.
Given equation: (3 + n) / m = b
Student 1's Work:
Step 1: Multiply both sides of the equation by m to eliminate the denominator.
Result: 3 + n = b * m
Student 2's Work:
Step 1: Subtract n from both sides of the equation.
Result: 3/m = b - n
Student 3's Work:
Step 1: Divide both sides of the equation by (3 + n).
Result: m = b / (3 + n)
Now, let's evaluate the solutions of each student:
Student 1's Solution (3 + n = b * m):
This solution is correct because student 1 correctly eliminated the denominator by multiplying both sides of the equation by m. This step maintains the integrity of the equation, providing a valid solution for m.
Student 2's Solution (3/m = b - n):
This solution is incorrect because student 2 attempted to eliminate the denominator by subtracting n from both sides of the equation. However, this approach is incorrect because n is added outside the parentheses, so it cannot be subtracted directly.
Student 3's Solution (m = b / (3 + n)):
This solution is incorrect because student 3 skipped the step of eliminating the denominator. They divided both sides of the equation by (3 + n) without considering the denominator m. As a result, this equation does not represent the original equation given.
In conclusion, student 1 solved the equation correctly by properly eliminating the denominator. Student 2 attempted an incorrect method of elimination, and student 3 skipped the necessary step, resulting in incorrect solutions.