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Look at Mia's work.

[tex]
\[
\begin{aligned}
83+n & =110 \\
83+83+n & =110+83 \\
n & =193
\end{aligned}
\]
[/tex]

What was Mia's error?

A. Mia's work is correct.

B. Mia made an addition error when adding 110 and 83.

C. Mia only needed to add 83 to 110.

D. Mia should have subtracted 83 from both sides of the equation.

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].

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