Math 017 Materials With Exercises

Lesson 10__________________________________________________________________________________Topics: Linear Inequalities; Graphing sets of the type x a , x a on a number line.__________________________________________________________________________________We will now be discussing inequalities.Meaning and symbolic notation for ‘less (greater) than’, ‘less (greater) than or equal to’Recall thatx < 2 means that a number x is less than 2x > 2 means that a number x is greater than 2.Notice, that x 2 has exactly the same meaning as 2 x , and x 2 the same as 2 x (just as 1 2has exactly the same meaning as 2 > 1).The following symbols are also in usex ≤ 2 means that a number x is less than or equal to 2x ≥ 2 means that a number x is greater than or equal to 2.Again, x 2 is equivalent to 2 x, x 2 is equivalent to 2 x.The only difference between „ x 2‟ and „ x 2‟ is that 2 satisfies the first inequality but does notsatisfy the second one (2 is not less than 2). Similarly, 2 satisfies ‘ x 2’, but does not satisfy ‘ x 2 ’.Example 10.1 Describe the following set of numbers using inequality signs.a) All numbers x that are positiveb) All numbers x that are non-negativec) All numbers x that are at most equal to 9d) All numbers x that are at least equal to 9e) All numbers x that are not less than 9Solution:a) x 0 (zero should not be included)b) x 0 (zero should be included)c) x 9 (at most means that amount or less)d) x 9 (at least means that amount or higher)e) x 9 (not less than includes the given number and higher)Example 10.2 Determine which of the following numbers satisfies the condition x 2. 4, 2.1, 2, 0.9, 0, 1Solution:95