Solve any maths problem

Step by step

1. \left(x - 1\right) \left(x + 2\right) \geq 0

   Start from the inequality.

2. x^{2} + x - 2 >= 0

   Move everything to the left so we compare against 0.

3. x = -2, x = 1

   Find the critical points: where the expression equals 0 (or is undefined). They split the number line into test intervals.

4. (-\infty,\, -2): +\;\;(-2,\, 1): -\;\;(1,\, \infty): +

   Test a point inside each interval to find the sign of the expression there.

5. \left(-\infty, -2\right] \cup \left[1, \infty\right)

   Keep the intervals whose sign satisfies the inequality (closed endpoints for ≤ / ≥, open for < / >).

6. \left(1 \leq x \wedge x < \infty\right) \vee \left(x \leq -2 \wedge -\infty < x\right)

   The same answer written as inequalities.