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

Answer 1

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

1. Solving \( x + 2 > 6 \): \[ x + 2 > 6 \] Subtract 2 from both sides: \[ x > 4 \]

2. Solving \( 3x > 6 \): \[ 3x > 6 \] Divide both sides by 3: \[ x > 2 \]

Now, we combine the results from both inequalities:

• From \( x + 2 > 6 \), we have \( x > 4 \).
• From \( 3x > 6 \), we have \( x > 2 \).

The more restrictive condition is \( x > 4 \). Therefore, the solution set for the combined inequalities is: \[ \boxed{(4, \infty)} \]

This means that \( x \) must be greater than 4.