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

Question

{x|x?}
Fill in the question mark

Answer 1

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

1. For the first inequality \( x + 2 > 6 \):

   \[ x + 2 > 6 \] \[ x > 6 - 2 \] \[ x > 4 \]

2. For the second inequality \( 3x > 6 \):

   \[ 3x > 6 \] \[ x > \frac{6}{3} \] \[ x > 2 \]

Now we will combine the results of both inequalities. The solution to the system of inequalities \( x + 2 > 6 \) and \( 3x > 6 \) is determined by the stricter condition because both conditions must be met at the same time.

The stricter condition is \( x > 4 \) since \( x > 2 \) is always satisfied when \( x > 4 \).

Thus, the solution set is:

\[ { x \mid x > 4 } \]

So, filling in the question mark:

\[ { x \mid x > 4 } \]