Answered

Get the information you need with the help of IDNLearn.com's extensive Q&A platform. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

In this activity, you'll analyze a student's process of solving an equation.

Question 1:

Lily solved the equation [tex]3x + 10 = -3x + 8[/tex]. The explanation of her process is shown. Select the text that shows an error in her process or justification of steps, if one exists:

1. I used the addition property of equality to achieve [tex]6x + 10 = 8[/tex].
2. I used the subtraction property of equality to achieve [tex]6x = -2[/tex].
3. I used the division property of equality to achieve the solution of [tex]x = -\frac{1}{3}[/tex].

There is no error in Lily's process or justification of steps.

Sagot :

GinnyAnsweridn
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].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.