How do you solve #(2x-1)(x+2)(x-4)<=0#?
The inequality holds for
Keep in mind the rule for multiplying:
- Positive times positive is positive;
- Positive times negative is negative;
- Negative times positive is negative;
- Negative times negative is positive.
Combining these rules, you can clearly see that a product of factors is negative if and only if there is an odd number of negative factors (in this case, one or all three).
So, the important points are