Solving Inequalities with Interval Notation

1. A.8 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. Inequalities – Set Notation {variable | condition } pipe { x|x  5} The set of all xsuch thatx is greater than or equal to 5. x < 2 x < 2 { x | } ( –∞, 2) x ≥ 2 [2, ∞) { x | x ≥ 2} 4 < x < 9 (4, 9) { x | 4 < x < 9}

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

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 + .5(10) = $15.00 10 + .5(60) = $40.00 15.00 ≤ x ≤ 40.00