Answer :
Let's take a closer look at how to solve the equation [tex]\(83 + n = 110\)[/tex] correctly and identify the error in Mia's work.
### Steps to Solve the Equation:
1. Initial Equation:
[tex]\[
83 + n = 110
\][/tex]
2. Goal:
Isolate the variable [tex]\(n\)[/tex] on one side of the equation.
3. Correct Operation:
To isolate [tex]\(n\)[/tex], we need to remove the 83 that is being added to [tex]\(n\)[/tex]. This can be done by subtracting 83 from both sides of the equation. So, we perform the subtraction like this:
[tex]\[
83 + n - 83 = 110 - 83
\][/tex]
4. Simplify:
The left side becomes just [tex]\(n\)[/tex] (since 83 - 83 is 0), and we simplify the right side:
[tex]\[
n = 110 - 83
\][/tex]
[tex]\[
n = 27
\][/tex]
### Identifying Mia's Error:
- Mia's original approach was to add 83 to both sides:
[tex]\[
83 + n + 83 = 110 + 83
\][/tex]
- Consequently, she incorrectly ended up with [tex]\(n = 193\)[/tex].
- Mia's correction should have involved subtracting 83 from both sides, as we demonstrated, to correctly solve for [tex]\(n\)[/tex].
### Conclusion:
The error in Mia's work is that she needed to subtract 83 from both sides of the equation instead of adding it. Therefore, the correct result for [tex]\(n\)[/tex] should be 27.
### Steps to Solve the Equation:
1. Initial Equation:
[tex]\[
83 + n = 110
\][/tex]
2. Goal:
Isolate the variable [tex]\(n\)[/tex] on one side of the equation.
3. Correct Operation:
To isolate [tex]\(n\)[/tex], we need to remove the 83 that is being added to [tex]\(n\)[/tex]. This can be done by subtracting 83 from both sides of the equation. So, we perform the subtraction like this:
[tex]\[
83 + n - 83 = 110 - 83
\][/tex]
4. Simplify:
The left side becomes just [tex]\(n\)[/tex] (since 83 - 83 is 0), and we simplify the right side:
[tex]\[
n = 110 - 83
\][/tex]
[tex]\[
n = 27
\][/tex]
### Identifying Mia's Error:
- Mia's original approach was to add 83 to both sides:
[tex]\[
83 + n + 83 = 110 + 83
\][/tex]
- Consequently, she incorrectly ended up with [tex]\(n = 193\)[/tex].
- Mia's correction should have involved subtracting 83 from both sides, as we demonstrated, to correctly solve for [tex]\(n\)[/tex].
### Conclusion:
The error in Mia's work is that she needed to subtract 83 from both sides of the equation instead of adding it. Therefore, the correct result for [tex]\(n\)[/tex] should be 27.
