Izzie made a mistake going from step 2 to step 3

Question

true or false

Answer 1

Without additional context regarding the specific steps Izzie took, it's impossible to determine whether the statement is true or false. Could you please provide more details about the steps in question?

Answer 2

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

Answer 3

Let's analyze Izzie's work step by step to see if she made a mistake transitioning from step 2 to step 3.

1. Step 1: She correctly expanded \(3(t + 1) - 4t \geq -5\) to get:
   \(3t + 3 - 4t \geq -5\), which simplifies to
   \(-t + 3 \geq -5\).
   (This step is correct.)

2. Step 2: She then has:
   \(-t + 3 \geq -5\).
   This is also correct.

3. Step 3: Izzie moves to:
   \(-t \geq -5 - 3\)
   which simplifies to
   \(-t \geq -8\), not \(-t \geq -2\).
   (This is the mistake. She incorrectly simplified \(-5 - 3\).)

4. Step 4: If she had the correct equation from Step 3, \(-t \geq -8\), the next step would be to multiply both sides by -1, which would flip the inequality sign:
   \(t \leq 8\).

So, as you asked, Izzie did make a mistake going from step 2 to step 3.

The answer is True.

Answer 4

Which graph represents the solutions to this inequality: 5n−3<3(n+1)

Answer 5

Let’s first solve the inequality \(5n - 3 < 3(n + 1)\) step by step.

1. Distribute the 3 on the right side: \[ 5n - 3 < 3n + 3 \]

2. Subtract \(3n\) from both sides: \[ 5n - 3n - 3 < 3 \] \[ 2n - 3 < 3 \]

3. Add 3 to both sides: \[ 2n < 6 \]

4. Divide both sides by 2: \[ n < 3 \]

The solution to the inequality is \(n < 3\).

Graph Representation

To represent this inequality on a number line:

• You would draw an open circle (or dot) at \(3\) to indicate that \(3\) is not included in the solution.
• The shading would extend to the left, indicating that \(n\) can take any value less than \(3\).

If you have specific graph options to choose from, look for the one with an open circle at \(3\) and shading extending to the left.