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Solving Linear Inequalities
1. Represent solutions to inequalities graphically and using set notation.
Graphing InequalitiesGraphing 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 NotationInequalities – 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
InequalitiesInequalities
[
Graph, then write interval notation and set-builder notation.
x ≥ 5
Interval Notation: [ 5, ∞)
x < –3
Interval Notation: (– ∞, –3)
)
InequalitiesInequalitiesGraph, 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 NOTATIONGRAPHING THE NUMBER SETS ON THE NUMBER LINE
GRAPH: -1 < x < 3
0 2 4 6-2-4-6
INTERVAL NOTATION (AND TYPE)
(-1, 3 ) Bounded & Open
ORDER and INTERVAL NOTATIONGRAPHING THE NUMBER SETS ON THE NUMBER LINE
GRAPH: -6 < x < -½
0 2 4 6-2-4-6
INTERVAL NOTATION (AND TYPE)
[-6, -½ ] Bounded & Closed
ORDER and INTERVAL NOTATIONGRAPHING THE NUMBER SETS ON THE NUMBER LINE
GRAPH: 0 < x < 2.3
0 2 4 6-2-4-6
INTERVAL NOTATION (AND TYPE)
( 0, 2.3 ] Bounded & Half-Open
ORDER and INTERVAL NOTATIONGRAPHING THE NUMBER SETS ON THE NUMBER LINE
GRAPH: x > -2
0 2 4 6-2-4-6
INTERVAL NOTATION (AND TYPE)
(-2, ∞) Unbounded &Open
ORDER and INTERVAL NOTATIONGRAPHING THE NUMBER SETS ON THE NUMBER LINE
GRAPH: x < 4.5
0 2 4 6-2-4-6
INTERVAL NOTATION (AND TYPE)
(- ∞, 4.5 ] Unbounded &Closed
ORDER and INTERVAL NOTATIONConverting between intervals and inequalities
Write (-2, 5) as an inequalityin set-builder notation
{x | -2 < x < 5}Open or Closed?
Open
ORDER and INTERVAL NOTATION
Write [-2, ∞) as an inequalityin set-builder notation
{x | x > -2}Open or Closed?
Closed
Converting between intervals and inequalities
ORDER and INTERVAL NOTATION
Write (-∞, 6) as an inequalityin set-builder notation
{x | x < 6}Open or Closed?
Open
Converting between intervals and inequalities