High School

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 :

Sure! Let's go through Mia's work step-by-step and identify the error.

Mia was given the equation:
[tex]\[ 83 + n = 110 \][/tex]

To solve for [tex]\( n \)[/tex], we should isolate the variable [tex]\( n \)[/tex] by following these steps:

1. Identify the Operation:
- The operation on the left side of the equation is addition of 83 and [tex]\( n \)[/tex].

2. Undo the Operation:
- To solve for [tex]\( n \)[/tex], we need to undo this addition. To do that, we subtract 83 from both sides of the equation.

3. Subtract 83 from Both Sides:
[tex]\[
83 + n - 83 = 110 - 83
\][/tex]

4. Simplify the Equation:
- On the left side, [tex]\( 83 - 83 \)[/tex] simplifies to 0, so you're left with:
[tex]\[ n = 110 - 83 \][/tex]

5. Calculate the Right Side:
[tex]\[ n = 27 \][/tex]

Mia made an error in her work by adding 83 to both sides instead of subtracting it. Therefore, the correct step should have been to subtract 83 from both sides of the equation to find the value of [tex]\( n \)[/tex]. Hence, Mia's error was that she should have subtracted 83 from both sides of the equation.

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