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
Choose which one is true and which is false:
Izzie should not have changed the inequality symbol from >_ to <_ True | False
Izzie made a mistake going from step 2 to step 3 True | False
Izzie made a mistake going from step 3 to step 4 True | False
The correct answer should have been t <_ 8 True | False
Izzie made no mistakes in solving this inequality True | False

Answer 1

there's one more question at the end

Answer 2

Let's evaluate Izzie's steps to determine the truth of each statement.

1. **Step 1: 3(t + 1) - 4t >_ -5**
- This simplifies to \( 3t + 3 - 4t > -5 \) which is correct.

2. **Step 2: -t + 3 > -5**
- This is correct as well; the equation simplifies correctly to this form.

3. **Step 3: -t > -2**
- This step is achieved by subtracting 3 from both sides: \( -t + 3 - 3 > -5 - 3 \), which simplifies to \( -t > -2 \). This is correct.

4. **Step 4: t ≤ 2**
- To isolate \( t \), when you multiply or divide by a negative number, you reverse the inequality sign. Thus, from \( -t > -2 \), when dividing by -1, the inequality should flip to \( t < 2 \). This is correct.

Now we can evaluate each of the statements:

1. **Izzie should not have changed the inequality symbol from >_ to <_**: False. She correctly changed the inequality symbol when dividing by -1.

2. **Izzie made a mistake going from step 2 to step 3**: False. There is no mistake in this transition.

3. **Izzie made a mistake going from step 3 to step 4**: False. She correctly flipped the inequality when dividing by -1.

4. **The correct answer should have been t <_ 8**: False. The correct solution based on the work done is \( t < 2 \).

5. **Izzie made no mistakes in solving this inequality**: True. She solved the inequality correctly.

### Summary of the Truth Values:
- Statement 1: False
- Statement 2: False
- Statement 3: False
- Statement 4: False
- Statement 5: True

Answer 3

Sure! Please provide the additional question, and I'll help you with it.