What is the solution set of x+2≥6 and 3x≥6 ?(1 point) {x|x() }

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 \( x + 2 \geq 6 \):

   \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 4 \]

2. Solve \( 3x \geq 6 \):

   \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq 2 \]

Now, we need to find the intersection of the two solution sets:

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

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

Thus, the solution set is:

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

This can also be written as:

\[ [4, \infty) \]