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

Question

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)
True False
Izzie made a mistake going from step 1 to step 2

The correct answer should have been t≤8

Izzie made no mistakes in solving this inequality

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

Izzie made a mistake going from step 3 to step 4

Izzie made a mistake going from step 2 to step 3

Answer 1

Let's analyze Izzie's work step by step:

1. Step 1: \( 3(t + 1) - 4t \geq -5 \) simplifies to \( 3t + 3 - 4t \geq -5 \). This is correct and simplifies to \( -t + 3 \geq -5 \).

2. Step 2: This matches Izzie's completion: \( -t + 3 \geq -5 \). This step is also correct.

3. Step 3: Izzie writes \( -t \geq -2 \). To isolate \( t \), you multiply or divide by -1, which reverses the inequality. So this step should become \( t \leq 2 \). This step is correct.

4. Step 4: She states \( t \leq 2 \). This is indeed the correct representation of the solution after considering the flipped inequality from Step 3.

Now let's evaluate the statements:

1. Izzie made a mistake going from step 1 to step 2: False. She did not make a mistake.

2. The correct answer should have been \( t \leq 8 \): False. The correct answer is \( t \leq 2 \).

3. Izzie made no mistakes in solving this inequality: True. She solved it correctly.

4. Izzie should not have changed the inequality symbol from \( \geq \) to \( \leq \): False. She appropriately changed the inequality when multiplying by -1.

5. Izzie made a mistake going from step 3 to step 4: False. There was no mistake in the transition from Step 3 to Step 4.

6. Izzie made a mistake going from step 2 to step 3: False. She did not make a mistake there.

Overall, Izzie's work is correct.