Sahil tried a solve an equation but couldn't reach to the correct answer .
Following were the steps performed by him to solve the expression .
Solve for n : 3n + 5 (n + 2) = 46
Step 1 : 3n + 5n + 10 = 46
Step 2 : 8n + 10 = 46
Step 3 : 8n = 56
Step 4 : n `= (56)/(8)` = 7
Find the INCORRECT step.

Options

A. Step 4
B. Step 3
C. Step 2
D. Step 1

Answer

To solve the equation \(3n + 5(n + 2) = 46\) and identify the incorrect step in Sahil's solution, let's go through the steps one by one.

### Step 1: Expand the equation
The original equation is:
\[ 3n + 5(n + 2) = 46 \]
We need to distribute \(5\) to both \(n\) and \(2\):
\[ 3n + 5n + 10 = 46 \]
This step is correct.

### Step 2: Combine like terms
Now, we combine the like terms \(3n\) and \(5n\):
\[ (3n + 5n) + 10 = 46 \]
This simplifies to:
\[ 8n + 10 = 46 \]
This step is also correct.

### Step 3: Isolate the term with \(n\)
Next, we want to isolate \(8n\) by moving \(10\) to the other side of the equation. We should subtract \(10\) from both sides:
\[ 8n = 46 - 10 \]
This simplifies to:
\[ 8n = 36 \]
Here, Sahil incorrectly wrote \(8n = 56\). This is the incorrect step.

### Step 4: Solve for \(n\)
Now, we can solve for \(n\):
\[ n = \frac{36}{8} = 4.5 \]
This gives us the correct value of \(n\).

### Conclusion
The incorrect step in Sahil's solution is **Step 3**, where he incorrectly stated \(8n = 56\) instead of the correct \(8n = 36\).