Interval Notation for Inequalities Goal: To be able to represent solutions to inequalities graphically and using interval notation.

Graphing Inequalities Parentheses/bracket method : Parentheses: endpoint is not included Bracket: endpoint is included ≤, ≥ x < 2 x ≥ 2 Open Circle/closed circle method: Open Circle: endpoint is not included Closed Circle: endpoint is included ≤, ≥ x < 2 x ≥ 2 If the variable is on the left, the arrow points the same direction as the inequality.

Inequalities – Interval Notation [( smallest, largest )] Parentheses: endpoint is not included Bracket: endpoint is included ≤, ≥ Infinity: always uses a parenthesis x < 2 x ≥ 2 ( –∞, 2) [2, ∞) 4 < x < 9 (4, 9) 3-part inequality

Inequalities [ Graph, then write interval notation and set-builder notation. x ≥ 5 Interval Notation:[ 5, ∞) x < –3 Interval Notation:(– ∞, –3) )

Inequalities Graph, then write interval notation and set-builder notation. 1 < a < 6 Interval Notation:( 1, 6 ) –7 < x ≤ 3 Interval Notation:(– 7, –3] ( ) ( ]

Rewrite in interval notation and graph X ≤ 5

ORDER and INTERVAL NOTATION GRAPHING THE NUMBER SETS ON THE NUMBER LINE GRAPH: -1 < x < INTERVAL NOTATION (AND TYPE) (-1, 3 ) Bounded & Open

ORDER and INTERVAL NOTATION GRAPHING THE NUMBER SETS ON THE NUMBER LINE GRAPH: -6 < x < -½ INTERVAL NOTATION (AND TYPE) [-6, -½ ] Bounded & Closed

ORDER and INTERVAL NOTATION GRAPHING THE NUMBER SETS ON THE NUMBER LINE GRAPH: 0 < x < INTERVAL NOTATION (AND TYPE) ( 0, 2.3 ] Bounded & Half-Open

ORDER and INTERVAL NOTATION GRAPHING THE NUMBER SETS ON THE NUMBER LINE GRAPH: x > INTERVAL NOTATION (AND TYPE) (-2, ∞ ) Unbounded & Open

ORDER and INTERVAL NOTATION GRAPHING THE NUMBER SETS ON THE NUMBER LINE GRAPH: x < INTERVAL NOTATION (AND TYPE) (- ∞, 4.5 ] Unbounded & Closed

ORDER and INTERVAL NOTATION Converting between intervals and inequalities Write (-2, 5) as an inequality in set-builder notation {x | -2 < x < 5} Open or Closed? Open

ORDER and INTERVAL NOTATION Write [-2, ∞) as an inequality in set-builder notation {x | x > -2} Open or Closed? Closed Converting between intervals and inequalities

ORDER and INTERVAL NOTATION Write (-∞, 6) as an inequality in set-builder notation {x | x < 6} Open or Closed? Open Converting between intervals and inequalities