Question

Izzie is trying to solve this inequality: 3(t+1)−4t≥−5

After she solves it, she shows it to you and asks you if she did it correctly.

This is the work she completed:

Step 1: 3t+3−4t≥−5

Step 2: −t+3≥−5

Step 3: −t≥−2

Step 4: t≤2



(12 points)
The correct answer should have been t≤8


Izzie made a mistake going from step 2 to step 3


Izzie made a mistake going from step 3 to step 4


Izzie should not have changed the inequality symbol from ≥
to ≤


Izzie made a mistake going from step 1 to step 2


Izzie made no mistakes in solving this inequality

Answer 1

Let's review Izzie's steps and see if she made any mistakes while solving the inequality.

The original inequality is:
\[ 3(t+1) - 4t \geq -5 \]

### Step 1
Distributing the 3:
\[ 3t + 3 - 4t \geq -5 \]

This step is correct.

### Step 2
Combining like terms:
\[ -t + 3 \geq -5 \]

This step is also correct.

### Step 3
Now, to isolate \( t \), Izzie subtracts 3 from both sides:
\[ -t \geq -5 - 3 \]
\[ -t \geq -8 \]

This means Izzie's Step 3 is incorrect. Instead of \( -2 \), she should have \( -8 \).

### Step 4
In this step, when she multiplied both sides by -1, she incorrectly changed the direction of the inequality:
From:
\[ -t \geq -8 \]
to:
\[ t \leq 8 \]

This step directly matches the correct inequality conclusion.

To summarize:
1. Izzie made a mistake from Step 2 to Step 3 where she combined the numbers incorrectly.
2. The final answer after fixing the steps should lead to \( t \leq 8 \) which Izzie did arrive at, but she had an error in the process.

### Conclusion:
The correct evaluation is **Izzie made a mistake going from step 2 to step 3.**