Describe and correct the error made in solving the literal equation at the right for n. 2m = -6n + 3. 2m + 3 = -6n. 2m + 3/-6 = n
first, it's a linear equation, not a literal equation!
2m = -6n + 3
2m -3 = -6n
(2m-3)/(-6) = n
or,
n = 1/2 - 1/3 n
The error made in solving the literal equation for n is the division of (2m + 3) by -6. This step should be equivalent to dividing both sides of the equation by -6, but the division was incorrectly applied to only the term (2m + 3) instead of the entire right side of the equation (-6n + 3).
To correct this error, you need to divide both sides of the equation by -6. Here's the correct step-by-step solution:
1. Start with the equation: 2m = -6n + 3
2. Add 6n to both sides to isolate the -6n term: 2m + 6n = 3
3. Divide both sides of the equation by -6 to solve for n: (2m + 6n)/-6 = 3/-6
4. Simplify the expression on the left side: n = (2m + 6n)/-6
5. Simplify the expression on the right side: n = -1/2m - n/2
6. Rearrange the equation to have n on one side: n + n/2 = -1/2m
7. Combine like terms on the left side: (3n/2) = -1/2m
8. Multiply both sides by 2/3 to solve for n: n = -1/3m
The error made in solving the literal equation for n is incorrect application of the division operation. Let's break it down:
Starting equation: 2m = -6n + 3
Error 1: "2m + 3 = -6n" - This is correct, as it involves moving the 3 term to the other side of the equation by adding it to both sides.
Error 2: "2m + 3/-6 = n" - This is where the error occurs. Dividing only the constant term by -6 is not correct. To solve for n, we need to divide the entire expression on the left side by -6, including both the 2m and 3 terms.
Correction: To solve for n correctly, we divide the entire expression on the left side by -6:
(2m + 3) / -6 = n
Now, we have the correct equation for n.