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