Mathematics SKE: STRAND F        UNIT F6  Solving Inequalities:  Text
            STRAND F: ALGEBRA
            Unit 6  Solving Inequalities
                   Text
                   Contents
                          Section
                            F6.1   Inequalities on a Number Line
                            F6.2   Solution of Linear Inequalities (Inequations)
                            F6.3   Inequalities Involving Quadratic Terms
                          *
                            F6.4   Graphical Approach to Inequalities
                          *
                            F6.5   Dealing With More Than One Inequality
                          *
             ©  CIMT,  Plymouth University
                                              Mathematics SKE,  Strand F        UNIT F6  Solving Inequalities:  Text
            F6 Solving Inequalities
           F6.1 Inequalities on a Number Line
                          An inequality involves one of the four symbols
                                                                  >,   ≥,   <   or   ≤
                          The following statements illustrate the meaning of each of them.
                                                    x > 1       :  x is greater than 1
                                                    x ≥−2 : x is greater than or equal to −2
                                                    x < 10 : x is less than 10
                                                    x ≤ 12 : x is less than or equal to 12
                          Inequalities can be represented on a number line, as shown in the following worked
                          examples.
                          Worked Example 1
                          Represent the following inequalities on a number line.
                          (a)     x ≥ 2                (b)     x < −1               (c)     −24< x ≤
                          Solution
                          (a)    The inequality,   x ≥ 2,  states that x must be greater than or equal to 2. This is
                                 represented as shown.
                                                      2101234
                                 Note that solid mark, •, is used at 2 to show that this value is included.
                          (b)    The inequality              states that x must be less than      .  This is represented as
                                                   x < −1                                      −1
                                 shown.
                                                       3      210123
                                 Note that a hollow mark,   o, is used at        to show that this value is not included.
                                                                             −1
                          (c)    The inequality                   states that x is greater than       and less than or equal
                                                   −24< x ≤                                      −2
                                 to 4.  This is represented as shown.
                                                                                              456
                                            3      210123
                                 Note that   o is used at −2 because this value is not included and • is used at 4
                                 because this value is included.
                          ©  CIMT, Plymouth University
                                                                            1
                                         Mathematics SKE,  Strand F        UNIT F6  Solving Inequalities:  Text
            F6.1
                       Worked Example 2
                       Write an inequality to describe the region represented on each number line below.
                       (a)
                                                                             4
                                       210123
                       (b)
                                       210123
                       Solution
                       (a)    The diagram indicates that the value of x must be less than or equal to 3, which
                              would be written as
                                                                  x ≤ 3
                       (b)    The diagram indicates that x must be greater than or equal to     and less than 3.
                                                                                            −1
                              This is written as
                                                               −≤13x <
                       Exercises
                       1.     Represent each of the inequalities below on a number line.
                              (a)    x > 3           (b)   x < 4            (c)   x > −1          (d)    x < 2
                              (e)    x ≥ 6           (f)   x ≥−4            (g)   x ≤ 3           (h)    x ≤ 1
                              (i)                    (j)                    (k)                   (l)
                                     24≤≤x                 −12< x ≤               −22<