What is the solution set of x+2≥6𝑥+2≥6 and 3x≥63𝑥≥6?(1 point)

To find the solution set of the given inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we will solve each inequality step by step.

### Inequality 1: \( x + 2 \geq 6 \)

1. Subtract 2 from both sides:
\[
x \geq 6 - 2
\]
\[
x \geq 4
\]

### Inequality 2: \( 3x \geq 6 \)

1. Divide both sides by 3:
\[
x \geq \frac{6}{3}
\]
\[
x \geq 2
\]

### Combined Solution Set

Now, we need to find the overlapping solution for both inequalities:

1. The first inequality gives us \( x \geq 4 \).
2. The second inequality gives us \( x \geq 2 \).

The more restrictive condition is \( x \geq 4 \).

### Conclusion

The solution set is:
\[
\{ x \mid x \geq 4 \}
\]

In interval notation, this can be represented as:
\[
[4, \infty)
\]