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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
The correct answer should have been t≤8, true or false

Izzie made a mistake going from step 2 to step 3, true or false

Izzie made a mistake going from step 3 to step 4, true or false

Izzie should not have changed the inequality symbol from ≥
to ≤, true or false

Izzie made a mistake going from step 1 to step 2
true or false

Izzie made no mistakes in solving this inequality, true or false

5 answers

Let's carefully review Izzie's steps and determine if she made any mistakes in solving the inequality \( 3(t+1)−4t≥−5 \).

Step 1: She correctly expanded the expression: \[ 3(t+1) - 4t \geq -5 \]

This simplifies to: \[ 3t + 3 - 4t \geq -5 \] So this step is correct.

Step 2: Continuing from Step 1: \[ 3t + 3 - 4t = -t + 3 \geq -5 \] This is also correct.

Step 3: From Step 2: To isolate \( -t \): \[ -t + 3 \geq -5 \] Subtract 3 from both sides: \[ -t \geq -8 \]

This was incorrectly simplified. So in this step, Izzie made a mistake. The correct inequality should be: \[ -t \geq -8 \] Now, multiplying both sides by -1 (which reverses the inequality): \[ t \leq 8 \]

Step 4: InIzzie's Step 4, she incorrectly solved: She said \( -t \geq -2 \) leads to \( t \leq 2 \), which is incorrect since she was wrong about what \( -t \) was equal to in the previous step.

Now, let's evaluate the statements:

  1. Izzie made a mistake going from step 2 to step 3: True
  2. Izzie made a mistake going from step 3 to step 4: True
  3. Izzie should not have changed the inequality symbol from ≥ to ≤: True (because she should have reversed the inequality when multiplying by -1)
  4. Izzie made a mistake going from step 1 to step 2: False (she was correct in step 1 to step 2)
  5. Izzie made no mistakes in solving this inequality: False (she made multiple mistakes)

So, the responses are:

  1. True
  2. True
  3. True
  4. False
  5. False
you missed one answer on which the correct answer should have been

Let's re-evaluate the questions and responses step by step.

  1. Izzie made a mistake going from step 2 to step 3: True

    • She incorrectly simplified \(-t + 3 \geq -5\) to \(-t \geq -2\); the correct progression is \(-t \geq -8\).

  2. Izzie made a mistake going from step 3 to step 4: True

    • Since she had already made an error in step 3, her conclusion in step 4 would also be incorrect.

  3. Izzie should not have changed the inequality symbol from ≥ to ≤: True

    • She did incorrectly multiply by -1 without reversing the inequality.

  4. Izzie made a mistake going from step 1 to step 2: False

    • Her work from step 1 to step 2 was correct.

  5. Izzie made no mistakes in solving this inequality: False

    • She made multiple mistakes throughout her work.

So, putting it all together, I can confirm my previous answers. However, if there was one more statement or aspect you wanted to address, please let me know specifically what you’re referring to, and I’ll be happy to help!

the one I was referring to was if the correct answer should have been t≤8

Thank you for your patience, and let’s clarify that specific point clearly.

After solving the inequality step by step:

Starting with: \[ 3(t+1) - 4t \geq -5 \] Step 1: \[ 3t + 3 - 4t \geq -5 \implies -t + 3 \geq -5 \] Step 2: Subtracting 3 from both sides gives: \[ -t \geq -8 \] Step 3: Multiplying both sides by -1 (which reverses the inequality): \[ t \leq 8 \]

So the final correct result is indeed \( t \leq 8 \).

Now we can address the statement:

  • "The correct answer should have been \( t \leq 8 \)": True

I apologize for not addressing that specific inquiry earlier. Thank you for pointing that out! If you have any further questions, feel free to ask!