zzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
Izzie made no mistakes in solving this inequality T/F
Izzie made a mistake going from step 3 to step 4 T/F
Izzie made a mistake going from step 1 to step 2 T/F
Izzie forgot to change the inequality symbol to be t≤8 T/F
Izzie should have had the answer t≤−8 T/F
Izzie made a mistake going from step 3 to step 4. The correct step 4 should be t ≤ 8, not t ≥ 8. The correct inequality is t ≤ 8, not t ≥ 8. Therefore, Izzie forgot to change the inequality symbol to be t ≤ 8. So the statement "Izzie forgot to change the inequality symbol to be t ≤ 8" is true.
zzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
Izzie made no mistakes in solving this inequality T/F
Izzie made a mistake going from step 3 to step 4 T/F
Izzie made a mistake going from step 1 to step 2 T/F
Izzie forgot to change the inequality symbol to be t≤8 T/F
Izzie should have had the answer t≤−8 T/F
I apologize for the incorrect response in my previous message.
Izzie made a mistake going from step 3 to step 4. The correct step 4 should be t ≤ 8, not t ≥ 8. Izzie made an error when she flipped the inequality symbol. The correct answer should be t ≤ 8. Therefore, the statement "Izzie made a mistake going from step 3 to step 4" is true.
The statement "Izzie made a mistake going from step 1 to step 2" is false. Izzie performed the correct simplification by distributing the 3 to both terms inside the parentheses.
The statement "Izzie forgot to change the inequality symbol to be t≤8" is true. Izzie mistakenly flipped the inequality symbol when she divided by -1.
The statement "Izzie should have had the answer t≤−8" is false. The correct answer is t ≤ 8, not t ≤ -8.
Overall, Izzie made one mistake in solving this inequality.
Izzie made no mistakes in solving this inequality. False.
Izzie made a mistake going from step 3 to step 4. True.
Izzie made a mistake going from step 1 to step 2. False.
Izzie forgot to change the inequality symbol to be t≤8. False.
Izzie should have had the answer t≤−8. False.
Izzie made a mistake going from step 3 to step 4 because she incorrectly flipped the inequality symbol.
Let's go through the steps to solve the inequality and determine if there are any other mistakes.
Step 1: Distribute the 3 to both terms inside the parentheses: 3(t + 1) - 4t ≥ -5
This gives us: 3t + 3 - 4t ≥ -5.
Izzie did not make a mistake going from step 1 to step 2.
Step 2: Combine like terms: 3t - 4t + 3 ≥ -5
This simplifies to: -t + 3 ≥ -5.
Izzie did not make a mistake going from step 2 to step 3.
Step 3: Subtract 3 from both sides of the inequality to isolate the variable: -t + 3 - 3 ≥ -5 - 3
This becomes: -t ≥ -8.
Izzie made a mistake going from step 3 to step 4 because she should have divided by -1, which would have required her to flip the inequality symbol. So, the correct step 4 should be: t ≤ 8.
Therefore, Izzie did make a mistake, and the correct answer is: Izzie made a mistake going from step 3 to step 4 (T/F).