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

Answer 1

Let's go through Izzie's steps to see if she solved the inequality correctly.

Starting from the original inequality:

1. **Original Inequality:**
\[ 3(t + 1) - 4t \geq -5 \]

2. **Step 1 - Distributing:**
\[ 3t + 3 - 4t \geq -5 \]
This step is correct.

3. **Step 2 - Combining like terms:**
\[ -t + 3 \geq -5 \]
This step is also correct.

4. **Step 3 - Isolating \(t\):**
\[ -t \geq -2 \]
This step is correct as well.

5. **Step 4 - Dividing by -1:**
When multiplying or dividing an inequality by a negative number, the direction of the inequality changes. Therefore, dividing both sides by -1 gives:
\[ t \leq 2 \]
This step is also correct, but it’s important to mention the change in the direction of the inequality.

So, Izzie correctly solved the inequality, and the final solution is:

\[ t \leq 2 \]

She did a good job!