Let's analyze the steps Brianna took to solve the equation [tex]\(0.1x + 3 = 1.7\)[/tex]:
1. Brianna starts correctly by recognizing that she needs to isolate [tex]\(x\)[/tex]. To do this, she should eliminate the [tex]\(+3\)[/tex] on the left side of the equation.
[tex]\[
(-3) + 0.1x + 3 = 1.7 + (-3)
\][/tex]
This step simplifies to:
[tex]\[
0.1x = -1.3
\][/tex]
So far, Brianna is correct up to this point (even though this argument technically also works with [tex]\(0.1x + 3 - (-3) = 1.7 - (-3)\)[/tex])
2. Her next step is where the mistake occurs. To solve for [tex]\(x\)[/tex] in [tex]\(0.1x = -1.3\)[/tex], the correct operation should be to divide both sides of the equation by [tex]\(0.1\)[/tex]:
[tex]\[
\frac{0.1x}{0.1} = \frac{-1.3}{0.1}
\][/tex]
This gives:
[tex]\[
x = -13
\][/tex]
However, Brianna incorrectly subtracts [tex]\(0.1\)[/tex] instead:
[tex]\[
(-0.1) + 0.1x = -1.3 + (-0.1)
\][/tex]
By doing this wrong operation which violates the properties, Brianna ends up with the incorrect result,
[tex]\[
x = -1.4
\][/tex]
Therefore, the mistake Brianna made is on Line 3. Instead of subtracting [tex]\(0.1\)[/tex], she should have divided both sides of the equation by [tex]\(0.1\)[/tex]. This is the correct identification of Brianna’s mistake.
