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
