Solve the following system of inequations:
`3x-1ge5,x+2gt-1`

Answer

To solve the system of inequations \(3x - 1 \geq 5\) and \(x + 2 > -1\), we will tackle each inequation step by step.

### Step 1: Solve the first inequation \(3x - 1 \geq 5\)

1. **Add 1 to both sides**:
\[ 3x - 1 + 1 \geq 5 + 1 \]
This simplifies to:
\[ 3x \geq 6 \]

2. **Divide both sides by 3**:
\[ x \geq \frac{6}{3} \]
This simplifies to:
\[ x \geq 2 \]

### Step 2: Solve the second inequation \(x + 2 > -1\)

1. **Subtract 2 from both sides**:
\[ x + 2 - 2 > -1 - 2 \]
This simplifies to:
\[ x > -3 \]

### Step 3: Combine the solutions

Now we have two inequalities:
1. \(x \geq 2\)
2. \(x > -3\)

To find the solution set, we need to consider the intersection of these two conditions.

- The first condition \(x \geq 2\) means that \(x\) can take any value starting from 2 and going to infinity.
- The second condition \(x > -3\) means that \(x\) can take any value greater than -3.

### Final Solution

The intersection of these two conditions is:
\[ x \geq 2 \]
Thus, the solution set is:
\[ x \in [2, \infty) \]