Let's carefully examine each of Lily's steps in solving the equation \(3x + 10 = -3x + 8\).
### Step 1
Lily claims:
"1. I used the addition property of equality to achieve \(6x + 10 = 8\)."
#### Checking Step 1:
To combine like terms, Lily would add \(3x\) to both sides of the equation:
[tex]\[
3x + 10 + 3x = -3x + 8 + 3x
\][/tex]
Simplifying both sides:
[tex]\[
6x + 10 = 8
\][/tex]
This step is correct. The result of this operation is indeed \(6x + 10 = 8\).
### Step 2
Lily claims:
"2. I used the addition property of equality to achieve \(6x = 18\)."
#### Checking Step 2:
The next logical step to isolate \(x\) is to subtract 10 from both sides:
[tex]\[
6x + 10 - 10 = 8 - 10
\][/tex]
Simplified, this would be:
[tex]\[
6x = -2
\][/tex]
So, the correct result should be \(6x = -2\), not \(6x = 18\). This step contains an error.
### Step 3
Lily claims:
"3. I used the subtraction property of equality to achieve the solution of \(x = \frac{1}{3}\)."
Given the incorrect step in the second part, this step should not be checked based on a false premise. However, theoretically, if she was correctly solving \(6x = -2\):
[tex]\[
x = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
So, there is an error in her process.
### Conclusion
Lily made an error in step 2 of her solution process. The correct justification should achieve [tex]\(6x = -2\)[/tex], not [tex]\(6x = 18\)[/tex].
