Izzie 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
(2 points)
True False
Izzie made no mistakes in solving this inequality
True – Izzie made no mistakes in solving this inequality
False – Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
True – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
True – Izzie made a mistake going from step 1 to step 2
False – Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
True – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
False – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
Izzie should have had the answer t≤−8
True – Izzie should have had the answer t is less than or equal to negative 8
False – Izzie should have had the answer t is less than or equal to negative 8
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The answer is:
False – Izzie made no mistakes in solving this inequality
To solve the inequality 3(t+1)-4t ≥ -5, let's go through the steps Izzie took:
Step 1: Distribute the 3 to the terms inside the parentheses.
3t + 3 - 4t ≥ -5
Step 2: Combine like terms.
-t + 3 ≥ -5
Step 3: Subtract 3 from both sides.
-t ≥ -8
Step 4: Since we have a negative coefficient (-1) multiplying t, we need to flip the inequality symbol when dividing both sides by -1.
t ≤ 8
Now, let's evaluate the given options:
Izzie made no mistakes in solving this inequality.
False – Izzie made a mistake going from step 3 to step 4. When dividing both sides by -1, the inequality symbol should be flipped.
Izzie made a mistake going from step 1 to step 2.
False – Izzie correctly combined like terms in step 2.
Izzie forgot to change the inequality symbol to be t ≤ 8.
True – Izzie correctly solved for t in step 4, but she forgot to change the inequality symbol to "less than or equal to."
Izzie should have had the answer t ≤ -8.
False – Izzie's final answer, t ≤ 8, is correct. There is no need to include negative 8 in the solution since the inequality is not "less than," but "less than or equal to."
Therefore, the correct answer is:
Izzie made a mistake going from step 3 to step 4.
False – Izzie made a mistake going from step 3 to step 4.