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

Answer 1

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

1. Solving \( x + 2 \geq 6 \): \[ x + 2 - 2 \geq 6 - 2 \quad \Rightarrow \quad x \geq 4 \]

2. Solving \( 3x \geq 6 \): \[ \frac{3x}{3} \geq \frac{6}{3} \quad \Rightarrow \quad x \geq 2 \]

Now we have two conditions:

• \( x \geq 4 \)
• \( x \geq 2 \)

Since \( x \geq 4 \) is the more restrictive condition, the solution set for both inequalities is: \[ x \geq 4 \]

In interval notation, the solution set is \( [4, \infty) \).