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

Question

{x|x𝑥|𝑥}

Answer 1

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: \[ [4, \infty) \]