What is the solution set of x + 2 > (a line is under both the > sign) 6 and 3x > 6?

Answer 1

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

1. First inequality:

   \[ x + 2 \geq 6 \]

   Subtract 2 from both sides:

   \[ x \geq 4 \]

2. Second inequality:

   \[ 3x > 6 \]

   Divide both sides by 3:

   \[ x > 2 \]

Now, we combine the solutions from both inequalities:

• From \( x \geq 4 \), we see that \( x \) can take values of 4 or greater.
• From \( x > 2 \), we see that \( x \) can take values of greater than 2.

Since \( x \geq 4 \) is the more restrictive condition (because any \( x \) that satisfies this will automatically satisfy the condition \( x > 2 \)), the overall solution set is:

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