Find the solution set of `3x-1ge5,x+2gt-1`.

Answer

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

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

1. Start by isolating the term with \(x\):
\[ 3x - 1 + 1 \geq 5 + 1 \]
This simplifies to:
\[ 3x \geq 6 \]

2. Next, divide both sides by 3:
\[ x \geq 2 \]

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

1. Isolate \(x\) by subtracting 2 from both sides:
\[ x + 2 - 2 > -1 - 2 \]
This simplifies to:
\[ x > -3 \]

### Step 3: Combine the results

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 inequalities.

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

### Final Solution Set

The solution set is determined by the more restrictive inequality, which is \(x \geq 2\). Therefore, the solution set is:
\[ \{ x \mid x \geq 2 \} \]
or in interval notation:
\[ [2, \infty) \]