Answer :
Let's look at Mia's work to solve the equation [tex]\(83 + n = 110\)[/tex].
Mia's process:
1. Starting equation: [tex]\(83 + n = 110\)[/tex]
2. In her solution, Mia added 83 to both sides:
[tex]\[
83 + 83 + n = 110 + 83
\][/tex]
3. This simplified to:
[tex]\[
n = 193
\][/tex]
Mia's approach was incorrect. Instead of adding 83 to both sides, she should have subtracted 83 from both sides to isolate [tex]\(n\)[/tex] and solve the equation.
Correct Steps:
1. Start with the original equation:
[tex]\[
83 + n = 110
\][/tex]
2. Subtract 83 from both sides to isolate [tex]\(n\)[/tex]:
[tex]\[
n = 110 - 83
\][/tex]
3. Calculate:
[tex]\[
n = 27
\][/tex]
Therefore, Mia's error was in adding instead of subtracting 83. The correct approach would have been to subtract 83 from both sides of the original equation to find that [tex]\(n = 27\)[/tex].
Mia's process:
1. Starting equation: [tex]\(83 + n = 110\)[/tex]
2. In her solution, Mia added 83 to both sides:
[tex]\[
83 + 83 + n = 110 + 83
\][/tex]
3. This simplified to:
[tex]\[
n = 193
\][/tex]
Mia's approach was incorrect. Instead of adding 83 to both sides, she should have subtracted 83 from both sides to isolate [tex]\(n\)[/tex] and solve the equation.
Correct Steps:
1. Start with the original equation:
[tex]\[
83 + n = 110
\][/tex]
2. Subtract 83 from both sides to isolate [tex]\(n\)[/tex]:
[tex]\[
n = 110 - 83
\][/tex]
3. Calculate:
[tex]\[
n = 27
\][/tex]
Therefore, Mia's error was in adding instead of subtracting 83. The correct approach would have been to subtract 83 from both sides of the original equation to find that [tex]\(n = 27\)[/tex].
