Answer :
Sure! Let's look at Jake's steps to solve the equation and see where there might be a mistake.
1. Step 1: Original Equation
[tex]\[
\frac{1}{3} x + 7 = 15
\][/tex]
The equation starts with [tex]\(\frac{1}{3} x + 7 = 15\)[/tex].
2. Step 2: Subtract 7 from Both Sides
Jake wrote:
[tex]\[
\frac{1}{3} x + 7 - 7 = 15
\][/tex]
Here, Jake tried to remove 7 from the left side, but he forgot to subtract 7 from the right side too. To maintain balance, the correct adjustment should be:
[tex]\[
\frac{1}{3} x + 7 - 7 = 15 - 7
\][/tex]
Which simplifies to:
[tex]\[
\frac{1}{3} x = 8
\][/tex]
3. Step 3: After Simplification of Step 2
Jake incorrectly showed:
[tex]\[
\frac{1}{3} x = 15
\][/tex]
However, the correct simplification based on the previous note should have led to:
[tex]\[
\frac{1}{3} x = 8
\][/tex]
4. Step 4: Multiply Both Sides by 3
Jake proceeded with:
[tex]\[
3 \cdot \frac{1}{3} x = 3 \cdot 15
\][/tex]
This step would correctly multiply both sides of the equation by 3, but based on his incorrect step 3, leading him to solve:
[tex]\[
x = 45
\][/tex]
If he had the correct step 3 ([tex]\(\frac{1}{3} x = 8\)[/tex]), then:
[tex]\[
3 \cdot \frac{1}{3} x = 3 \cdot 8
\][/tex]
Which would simplify to:
[tex]\[
x = 24
\][/tex]
5. Step 5: Incorrect Value of x
Jake concluded with:
[tex]\[
x = 45
\][/tex]
But based on correcting the process, the actual solution should have been [tex]\(x = 24\)[/tex] if the mistake in step 2 were corrected appropriately.
Therefore, the error Jake made occurred in step 2, where he forgot to subtract 7 from both sides, leading to subsequent incorrect steps. With this analysis, we can conclude that the statement that Jake made a mistake in step 2 is true, which aligns with option A.
1. Step 1: Original Equation
[tex]\[
\frac{1}{3} x + 7 = 15
\][/tex]
The equation starts with [tex]\(\frac{1}{3} x + 7 = 15\)[/tex].
2. Step 2: Subtract 7 from Both Sides
Jake wrote:
[tex]\[
\frac{1}{3} x + 7 - 7 = 15
\][/tex]
Here, Jake tried to remove 7 from the left side, but he forgot to subtract 7 from the right side too. To maintain balance, the correct adjustment should be:
[tex]\[
\frac{1}{3} x + 7 - 7 = 15 - 7
\][/tex]
Which simplifies to:
[tex]\[
\frac{1}{3} x = 8
\][/tex]
3. Step 3: After Simplification of Step 2
Jake incorrectly showed:
[tex]\[
\frac{1}{3} x = 15
\][/tex]
However, the correct simplification based on the previous note should have led to:
[tex]\[
\frac{1}{3} x = 8
\][/tex]
4. Step 4: Multiply Both Sides by 3
Jake proceeded with:
[tex]\[
3 \cdot \frac{1}{3} x = 3 \cdot 15
\][/tex]
This step would correctly multiply both sides of the equation by 3, but based on his incorrect step 3, leading him to solve:
[tex]\[
x = 45
\][/tex]
If he had the correct step 3 ([tex]\(\frac{1}{3} x = 8\)[/tex]), then:
[tex]\[
3 \cdot \frac{1}{3} x = 3 \cdot 8
\][/tex]
Which would simplify to:
[tex]\[
x = 24
\][/tex]
5. Step 5: Incorrect Value of x
Jake concluded with:
[tex]\[
x = 45
\][/tex]
But based on correcting the process, the actual solution should have been [tex]\(x = 24\)[/tex] if the mistake in step 2 were corrected appropriately.
Therefore, the error Jake made occurred in step 2, where he forgot to subtract 7 from both sides, leading to subsequent incorrect steps. With this analysis, we can conclude that the statement that Jake made a mistake in step 2 is true, which aligns with option A.
