a3 1.7a interval notation, intersection and union of intervals, solving one variable inequalities...
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A3 1.7a Interval Notation, Intersection and Union of Intervals,
Solving One Variable Inequalities
Homework: p. 195-196 1-45 odd
Interval NotationSolve and report answer graphically.
Interval Notation: Graph:
3 10x
( , ) { | }a b x a x b
[ , ] { | }a b x a x b
( , ) { | }a x x a
( , ] { | }b x x b
Using Interval NotationExpress each interval in set-builder notation and graph.
( 1,4]
[2.5,4]
( 4, )
Intersections and Unions of Intervals
Use graphs to find the solution set:
intersection=overlap
= union=everything
(1,4) [2,8]
(1,4) [2,8]
(2,6) [1,3]
(2,6) [1,3]
Solving Linear Inequalities in One VariableManage the equation as an equality , then bring in the inequality signs.
Remember: if you multiply or divide by a negative number while solving, the inequality sign switches!
Guided PracticeSolve. Report answers in interval notation.
1. 3 2 11x 2. 2 4 5x x
3. 3 1 7 15x x 3 2 1
4. 4 3 4
x x
Inequalities with unusual solution sets…
1. 2( 4) 2 3x x
2. 1 1x x
Whiteboard Problems:Express the interval notation in set-builder notation:
Solve:
Solve. Express answer in interval notation.
1. ( 2,4] 2. [ 2,5]
3. ( 4,0) [ 2,1] 4. ( ,6) [2,9]
5. 2 5<17x 6. 18 45 12 8x x
4 3 2 17. 2
6 12
x x