Izzie is trying to solve this inequality: 3(t+1)−4t≥−5

Question

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!