How close to -1 do we have to take x so that the following inequality is satisfied?

Question

1/(x+1)^2>100

| x - (-1) | <

Answer 1

1/(x + 1)^2 &gt; 100

(x + 1)^2 &lt; 1/100

|x + 1| &lt; 1/10

|x - (-1)| &lt; 1/10

so x must be within 1/10, or 0.1, of -1 for the inequality to hold.