What is the solution set of x+2≥6 and 3x≥6 ?(1 point) {x|x() }

To find the solution set for the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we will solve each inequality separately.

1. **Solve \( x + 2 \geq 6 \)**:

\[
x + 2 \geq 6
\]
Subtract 2 from both sides:
\[
x \geq 4
\]

2. **Solve \( 3x \geq 6 \)**:

\[
3x \geq 6
\]
Divide both sides by 3:
\[
x \geq 2
\]

Now, we need to find the intersection of the two solution sets:

- From the first inequality, \( x \geq 4 \).
- From the second inequality, \( x \geq 2 \).

The solution set that satisfies both inequalities is determined by the more restrictive condition, which is \( x \geq 4 \).

Thus, the solution set is:

\[
\{ x \mid x \geq 4 \}
\]

This can also be written as:

\[
[4, \infty)
\]