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. Solve the first inequality: \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 6 - 2 \] \[ x \geq 4 \]

2. Solve the second inequality: \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq \frac{6}{3} \] \[ x \geq 2 \]

3. Combine the solution sets: We now have two inequalities:

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

   The solution to the system of inequalities is the intersection of these two conditions. The more restrictive condition is \( x \geq 4 \).

Thus, the solution set is: \[ \boxed{x \geq 4} \]