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

Answer 1

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

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

2. Solving the second inequality: \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq \frac{6}{3} \] Simplifying gives: \[ x \geq 2 \]

Now, we combine the two solutions:

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

The solution set must satisfy both inequalities. The more restrictive condition is \( x \geq 4 \).

Therefore, the solution set of the given inequalities is: \[ { x \mid x \geq 4 } \]

This can also be expressed in interval notation as: \[ [4, \infty) \]