Answered

Brianna solved a two-step equation, but she made a mistake along the way.

[tex]\[
\begin{array}{l}
0.1x + 3 = 1.7 \\
(-3) + 0.1x + 3 = 1.7 + (-3) \quad \text{Line 1} \\
0.1x = -1.3 \quad \text{Line 2} \\
(-0.1) + 0.1x = -1.3 + (-0.1) \quad \text{Line 3} \\
x = -1.4 \quad \text{Line 4} \\
\end{array}
\][/tex]

What mistake did Brianna make?

A. On Line 1, Brianna should have subtracted 3 instead of adding -3.
B. On Line 1, Brianna violated the addition property of equality.
C. On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
D. On Line 3, Brianna violated the addition property of equality.



Answer :

GinnyAnswer
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.