Compound Inequalities If we have two sets A and B, then we say that an element belongs to A and B if it belongs to both of them.  For example, a student may belong to the honor society if that student is a member of A and B where         A = the collection of all registered students         B = the collection of all student has a GPA of at least 3.0. Your instructor cannot belong to the honor society, since he is not a student.   Example If         A  =  {x | x > -2} and         B  =  {x | x <1} then A and B is the in between part of the number line.         A and B  =  {x | -2 < x < 1} Exercises   Write the following on a number line: 3x - 4 < 2 and 2x + 5 > 1 5x - 2 < 3 and 4x + 7 > 3 3x - 4 < 2 and 2x - 7 > 5 If we have two sets A and B, then we say that an element belongs to A or B is it belongs to either of them.  For example, a person can get a back seat pass to a concert if that person belongs to A or B where         A  =  set of people that know the band member personally.         B  =  set of people that sit in the VIP seats. We always have          (A and B)  C  (A or B)   Example:   If         A  =  {x | x < -1)         B  =  {x | x > 2} then A or B are the arrows left from -1 and right from 2. Exercises   Sketch the solution set on a number line. 3x + 2  >  4    or    5x + 7  <  2 x - 10  >  5    or    3x + 2  <  5 4x - 2  >  2    or    5x + 1  <  11 2x - 1  <  1    or    3x  + 5  >  8   We also use intersection (I) for and and union (U) for or. Double Inequalities We can write a compound inequality as a double inequality as in the example         -3  <  2x + 5  <  7 This can be written as a compound inequality by writing         -3  <  2x + 5  and  2x + 5  <  7         -8  <  2x  and  2x  <  2                    Subtracting 5         -4  <  x  and  x  <  1                        Dividing by 2 Exercise Write the double inequality as a compound inequality and then solve it. -5  <  3x + 4  <  19 2y - 1  <  y + 2  <  6y + 12 15 - t  <  t + 15  <  9t - 9 h + 1  <  2/3 h  <  h - 2