1. Interval Notation; Solving Inequalities
Students will be able to (swbat):
1. Represent Solutions to Inequalities Graphically, and by Using Set & Interval Notation.
2. Solve Linear, Combined, and Absolute Value Inequalities.

2. Inequalities – Interval Notation
If the variable is on the left, the arrow points the same direction as the inequality.
[( smallest, largest )]
Parentheses: endpoint is not included <, >
Bracket: endpoint is included ≤, ≥
Infinity: always uses a parenthesis
x < 2
( –∞, 2)
x ≥ 2
[2, ∞)
4 < x < 9
3-part inequality
(4, 9)

3. The set of all x such that x is greater than or equal to 5.
Inequalities – Set Notation
{variable | condition }
pipe
{ x | x  5}
The set of all x such that x is greater than or equal to 5.
x < 2
x < 2
( –∞, 2)
{ x | }
x ≥ 2
[2, ∞)
{ x | x ≥ 2}
4 < x < 9
(4, 9)
{ x | 4 < x < 9}

4. Inequalities
Graph, then write in interval and set notation. 1 < a < 6
Interval Notation: (-7,3]
Set Notation: {x }|

5. Solving Inequalities
If we multiply (or divide) by a negative, reverse the direction of the inequality!!!!!

6. Solving Inequalities
Solve then graph the solution and write it in interval notation and set notation. ]
Interval Notation:
(– ∞, –3 ]
Set Notation:
{ k | k ≤ –3 }

7. Solving Combined Inequalities
Solve the inequality 4 ≤ 2x + 2 ≤ 10, graph your solution, and write your solution in both interval and set notation.

8. Inequalities Involving Absolute Value
│x│< a is equivalent to -a < x < a (-a,a) │x│≤ a is equivalent to -a ≤ x ≤ a [-a,a] │x│> a is equivalent to x< -a or x>a (-∞,-a)U(a,∞) │x│≥ a is equivalent to x≤ -a or x≥a (-∞,-a]U[a,∞)

9. Solving an Absolute Value Inequality
Solve │2u + 5 │≤ 7, graph the solution set, and write the solution in both set and interval notation.

10. Methacton Merchandise
The Methacton Merchandise salesperson is paid a commission of $10 plus 50% of the selling price in excess of the cost to make the merchandise (owner’s cost). The owner of Methacton Merchandise claims that her products sell for at least owner’s cost plus $10 and at most owner’s cost plus $60. For each sale made, over what range can the salesperson expect the commission to vary?

11. Methacton Merchandise
(10) = $ (60) = $ ≤ x ≤ 40.00