College

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 :

Mia made an error in her method for solving the equation [tex]\(83 + n = 110\)[/tex].

Here's how to solve it correctly:

1. Original Equation:
[tex]\[
83 + n = 110
\][/tex]

2. Step to Isolate [tex]\(n\)[/tex]:
To solve for [tex]\(n\)[/tex], we need to isolate it. This means getting [tex]\(n\)[/tex] by itself on one side of the equation. To do this, we subtract 83 from both sides of the equation:

[tex]\[
83 + n - 83 = 110 - 83
\][/tex]

3. Simplifying Both Sides:
After subtracting, we simplify each side:

Left side: [tex]\(83 - 83 + n = n\)[/tex]
Right side: [tex]\(110 - 83 = 27\)[/tex]

4. Solution for [tex]\(n\)[/tex]:
Thus, we find:

[tex]\[
n = 27
\][/tex]

So, the mistake Mia made was that she added 83 instead of subtracting it from both sides of the equation. The correct result shows that [tex]\(n = 27\)[/tex].

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