There are four symbols that are used for inequalities.  < means is less than. So if we want to write 2 is less than 3 we write 2 < 3.  > means is more than, so 5 is more than 2 we write 5 > 2.  ≤ means is less than or equal to. This is used when we are looking at a set of numbers such as when the cost can be no more than 7 is written as c ≤ 7.  ≥ means is more than or equal to. So if the amount is at least 4, we write a ≥ 4.

The properties of Addition and Subtraction for inequalities work exactly the same as they did for equations: To check an inequality we must pick a number that fits into the solution set

Multiplication and Division properties of Inequalities act normal when dealing with a positive variable but when the variable is negative or has a negative coefficient then they act a little differently. For example, when we solve this equation normally the check doesn’t work. Why?

WRONG ANSWERRIGHT ANSWER The only difference is that the inequality sign is reversed. From this we can make a rule to use when working with negative coefficients when solving inequalities

In short, if the coefficient is positive the inequality sign stays the same, if the coefficient is negative then the inequality sign reverses direction.

Given inequality Distributive Property Addition Property of Inequalitites Subtraction Property of Inequalitites Division Property of Inequalities Since we divided by a negative 2 we had to reverse the inequality sign