The solution of the inequality (x+1)/(x+2) ≥ 1 is:

The correct answer is Option (4) → \((-\infty, -2)\)

The sign of x + 2 is not known, so the inequality cannot be multiplied by it. Bringing everything to one side:

    \( \displaystyle \frac{x+1}{x+2} - 1 \ge 0 \)

    \( \displaystyle \frac{x + 1 - (x + 2)}{x+2} \ge 0 \)

    \( \displaystyle \frac{-1}{x+2} \ge 0 \)

The numerator is −1, so the fraction is never zero, and it is positive only when the denominator is also negative:

    \( x + 2 \lt 0 \)

    \( x \lt -2 \)

So the solution set is \((-\infty, -2)\).

Tip: x = −2 is never part of the answer: it makes the denominator zero, so the expression is not defined there. That is why \((-\infty, -2]\), Option (2), is wrong even though the sign is \(\ge\).