Originally Posted by

**HallsofIvy** Well, first, ALL numbers satisfy "(x< 7) or (x> -2)" since every number that is NOT less than 7 is larger than -2.

If x is greater than 7 then it is **also** greater than -2. If x is less than -2 then it is also less than 7.

You should have learned in basic arithmetic: the product of any two positive numbers is positive and the product of any two negative numbers is also positive. In order that the product be negative, the two numbers must be of opposite sign.

You seem not to understand what "inequality" **means**. The numbers -3 and -4 satisfy x< -2/3 and x< 3 but have the same signs. The "endpoints", -2/3, and 3, are not the only numbers you need to look at. In fact, "x< -2/3 and x< 3" is exactly the **same** as "x< 3" by itself. If you do not understand that, you do not understand what "<" means.