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


1. Izzie made a mistake going from step 2 to step 3. Is this true or false?

2. Izzie made a mistake going from step 3 to step 4. Is this true or false?

3. Izzie should not have changed the inequality symbol from ≥
to ≤ . Is this true or false?

4. Izzie made a mistake going from step 1 to step 2. Is this true or false?

5. The correct answer should have been t≤8. Is this true or false?

6. Izzie made no mistakes in solving this inequality. Is this true or false?

Answer 1

1. False. Izzie did not make a mistake going from step 2 to step 3. She correctly multiplied both sides of the inequality by -1, which requires reversing the inequality symbol.
2. False. Izzie correctly solved the inequality in step 3 by multiplying both sides by -1. Therefore, she did not make a mistake going from step 3 to step 4.
3. False. Izzie correctly changed the inequality symbol from ≥ to ≤ in step 4 when she multiplied both sides of the inequality by -1.
4. True. Izzie made a mistake going from step 1 to step 2. She incorrectly combined the terms 3t and -4t, which should result in -t, not -1t.
5. False. The correct answer is t ≤ 2, not t ≤ 8. Izzie solved the inequality correctly.
6. False. Izzie made a mistake going from step 1 to step 2. Therefore, she did not solve the inequality correctly.