Решить не равенство х(х+10) (х-3) <0

To solve the inequality х(х+10)(х-3) <0, you can use the method of intervals.

1. Find the critical points by setting each factor equal to zero: х = 0, х = -10, х = 3.

2. Draw a number line and mark these critical points on it.

3. Test a value from each interval on the inequality to determine the sign of the expression.

   For х < -10, try х = -11, for example: (-11)(-11+10)(-11-3) = (11)(-1)(-14) = 154 > 0

   For -10 < х < 0, try х = -5, for example: (-5)(-5+10)(-5-3) = (-5)(5)(-8) = 200 > 0

   For 0 < х < 3, try х = 1, for example: (1)(1+10)(1-3) = (1)(11)(-2) = -22 < 0

   For х > 3, try х = 4, for example: (4)(4+10)(4-3) = (4)(14)(1) = 56 > 0

4. Determine the intervals where the inequality is true by looking for sign changes.

   The inequality is true for х < -10 and 0 < х < 3.

Therefore, the solution to the inequality is х < -10 or 0 < х < 3.