Question

The number of integers $n$ satisfying $-n + 2 \ge 0$ and $2n \ge 4$ is:

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

When working with compound inequalities, always solve each condition independently and then find the intersection of the solution sets.

Answer 1

The Correct Option is B

Step 1: Solve each inequality separately First inequality: \[ -n + 2 \ge 0 \Rightarrow -n \ge -2 \Rightarrow n \le 2 \] Second inequality: \[ 2n \ge 4 \Rightarrow n \ge 2 \] Step 2: Combine both inequalities From above, \[ n \ge 2 \quad \text{and} \quad n \le 2 \Rightarrow n = 2 \] Step 3: Count the number of integers Only one integer satisfies both conditions: \[ \boxed{1} \]