Nisha did the work below to solve an equation.

Step 1:
[tex]\[ 7b + 3.2b - 5 = 18.92 \][/tex]

Step 2:
[tex]\[ 10.2b - 5 = 18.92 \][/tex]

Step 3:
[tex]\[ 10.2b = 23.92 \][/tex]

Step 4:
[tex]\[ b = 2.345 \][/tex]

In which step did Nisha make her first error?

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



Answer :

Let's carefully examine Nisha's steps to identify any mistakes and to find out where she made her first error.

### Step-by-Step Solution

#### Step 1:
[tex]\[ 7b + 3.2b - 5 = 18.92 \][/tex]

In this step, Nisha combines the terms involving [tex]\( b \)[/tex] correctly:
[tex]\[ 7b + 3.2b = 10.2b \][/tex]

This gives us:
[tex]\[ 10.2b - 5 = 18.92 \][/tex]

This part is correct. No error here.

#### Step 2:
[tex]\[ 10.2b - 5 = 18.92 \][/tex]

Now, Nisha needs to isolate [tex]\( b \)[/tex]. First, she adds 5 to both sides of the equation:
[tex]\[ 10.2b = 18.92 + 5 \][/tex]
[tex]\[ 10.2b = 23.92 \][/tex]

This is also correct because adding 5 to both sides is the right step. No error so far.

#### Step 3:
[tex]\[ 5.2b = 18.92 \][/tex]

Here, Nisha seems to have made an error. After adding 5 to both sides in Step 2, she should divide both sides by 10.2 to isolate [tex]\( b \)[/tex]:
[tex]\[ b = \frac{23.92}{10.2} \][/tex]

But Nisha did:
[tex]\[ 5.2b = 18.92 \][/tex]

This is incorrect. Therefore, she made her first error in this step.

#### Step 4:
[tex]\[ b = 3.64 \][/tex]

Since Step 3 contains an error, the value of [tex]\( b \)[/tex] derived in this step is also incorrect. Let's find the correct value of [tex]\( b \)[/tex]:

From Step 2:
[tex]\[ 10.2b = 23.92 \][/tex]

Dividing both sides by 10.2:
[tex]\[ b = \frac{23.92}{10.2} \][/tex]
[tex]\[ b \approx 2.34 \][/tex]

To summarize:

- Correct Process:
- Combine like terms: [tex]\( 7b + 3.2b = 10.2b \)[/tex]
- Move constant to the other side: [tex]\( 10.2b - 5 = 18.92 \rightarrow 10.2b = 23.92 \)[/tex]
- Solve for [tex]\( b \)[/tex]: [tex]\( b = \frac{23.92}{10.2} \approx 2.34 \)[/tex]

Nisha made her first error at Step 3. The correct value of [tex]\( b \)[/tex] should have been found by:
[tex]\[ 10.2b = 23.92 \][/tex]
[tex]\[ b \approx 2.34 \][/tex]

First Error: Step 3