What is the solution set of x+2≥6 and 3x≥6?

To solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we will solve each inequality separately and then combine the solutions.

1. **Solve \( x + 2 \geq 6 \)**:
\[
x + 2 \geq 6
\]
Subtract 2 from both sides:
\[
x \geq 6 - 2
\]
\[
x \geq 4
\]

2. **Solve \( 3x \geq 6 \)**:
\[
3x \geq 6
\]
Divide both sides by 3:
\[
x \geq \frac{6}{3}
\]
\[
x \geq 2
\]

Now we have two inequalities:
- \( x \geq 4 \)
- \( x \geq 2 \)

The more restrictive condition is \( x \geq 4 \) since it is a higher lower bound.

Thus, the solution set is:
\[
\{ x \mid x \geq 4 \}
\]
In interval notation, this can be expressed as:
\[
[4, \infty)
\]