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

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. Solving the first inequality: \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 4 \]

2. Solving the second inequality: \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq 2 \]

3. Finding the solution set: The solution to each inequality is:

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

   Now, we need the intersection of these two solution sets. The more restrictive inequality is \( x \geq 4 \), so it encompasses the solution to both inequalities.

Thus, the solution set that satisfies both inequalities is: \[ { x ,|, x \geq 4 } \]

In interval notation, the solution set is: \[ [4, \infty) \]