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

Answer 1

To solve 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:

   \[ x \geq 4 \]

2. Solve the second inequality:

   \[ 3x \geq 6 \]

   Divide both sides by 3:

   \[ x \geq 2 \]

3. Find the solution set:

   The first inequality gives us \( x \geq 4 \), and the second gives us \( x \geq 2 \).

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

Thus, the final solution set is

\[ \boxed{[4, \infty)} \]