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
True or False
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

The correct answer should have been t≤8

Izzie made no mistakes in solving this inequality

Answer 1

To solve the inequality correctly, let's go through each step:

Step 1: Distribute the 3 to both terms inside the parentheses:
3(t+1) - 4t ≥ -5
3t + 3 - 4t ≥ -5

Step 2: Combine like terms:
-t + 3 ≥ -5

So far, so good. However, Izzie made a mistake in going from step 2 to step 3. When multiplying or dividing both sides of an inequality by a negative number, the inequality symbol should be reversed.

Step 3: Multiply both sides by -1 (and reverse the inequality):
-t ≤ -2

Now, Izzie made another mistake by changing the inequality symbol from ≤ to ≥. It should remain as ≤ since we multiplied both sides by a negative number.

So, the correct answer should be: -t ≤ -2

Finally, solving for t, we need to multiply both sides by -1 again. Remember to reverse the inequality symbol again since we are multiplying by a negative number.

Step 4: Multiply both sides by -1 (and reverse the inequality):
t ≥ 2

Therefore, the correct answer is t ≥ 2.

Izzie made mistakes going from step 2 to step 3 and in changing the inequality symbol from ≥ to ≤.

Answer 2

Its true or false

Answer 3

False. Izzie made a mistake going from step 2 to step 3 and also made a mistake in changing the inequality symbol from ≥ to ≤.