Question

In which set are all of the numbers solutions to the inequality x < -3?

Answer 1

Don’t you just love inequalities?  Of course I can only hear you saying “not really…inequalities stink!”  Well I know you may not like inequalities but you need to know how to work with them.   All right let me stress some points:

* the solution to an inequality is more than a single number;  inequalities have solution sets (many/infinite number of solutions).   As an example lets consider the inequality   x > 5  what can the value of x be?  i.e. what numbers are greater than 5? clearly an infinite amount of numbers are greater than 5 so we need to express the solutions to inequalities in a different way other than writing out all the numbers greater than 5 – that would take a lot of paper and with global warming….you get the idea.    So to deal with this little issue we graph the solution of an inequality on a number line.

other important points:

*  we simplify inequalities using the same steps as solving equations

* when dividing/multiplying both sides of an inequality by a negative number you need to reverse the inequality symbol; example  >  would turn into < .

* when graphing your solution <, > symbols use open circles;  <=,  >= symbols fill in the circle.

* make sure you can solve linear equations before taking on inequalities- good luck and may the force be with you!!