 Multiplying or Dividing by a POSITIVE number. › General Rule:  The symbols (>, <, ≤, ≥) STAY THE SAME.  When you have numbers a and b and c > 0,  If a > b, then ac > bc  If a < b, then ac < bc  If a > b, then a/c > b/c  If a < b, then a/c < b/c

› Examples:  Multiplication  4 > -1, so 4(5) > (-1)(5)20 > -5  -6 < 3, so (-6)(5) < (3)(5)-30 < 15  Division  6 > 4, so 6/2 > 4/23 > 2  2 < 8, so 2/2 < 8/21 < 4

 Multiplying or Dividing by a NEGATIVE number. › General Rule  The symbols (>, <, ≤, ≥) REVERSE.  When you have numbers a and b and c < 0  If a > b, then ac < bc  If a bc  If a b/c  If a > b, then a/c < b/c

› Example:  Multiplication  4 > -1, so 4(-2) < (-1)(-2)-8 < 2  -6 (3)(-2)12 > -6  Division  6 > 4, so 6/(-2) < 4/(-2)-3 < -2  2 8/(-2)-1 > -4

 Use a number line to graph inequalities. › Graph x/2 < -1  Multiply each side by 2.  (2)(x/2) < (2)(-1)  X < –

 When inequalities use symbols, an OPEN circle is used when graphing on a number line.  If solution has <, draw the arrow to the left of the OPEN circle.  If solution has >, draw the arrow to the right of the OPEN circle.

 When inequalities use ≤ or ≥ symbols, a CLOSED circle is used when graphing on a number line.  If a solution has a ≤, draw the arrow to the left of the CLOSED circle.  If a solution has a ≥, draw the arrow to the right of the CLOSED circle.

 Look for these WORD CLUES to help you determine which inequality symbol to use. ><≥≤ Is more than Is greater than Is larger than Above Is less than Is smaller than Below Minimum At least No less than No smaller than Maximum At most No greater than No more than