1. Solving Inequalities Using Addition and Subtraction Lessons 3-1 and 3-2

2. Addition Property of Inequalities – If any number is ________________ to each side of a true ___________________, the resulting inequality is also ________________. Example A 3 -5 3 + 2 -5 + 2 _____ _____ added equation true > > >5-3

3. Example Bn – 12 < 65 n – 12 +12 < 65 + 12Work inequalities horizontally. n < 77 “Open” circle (unshaded) at 77, then shade to the left (because it is “less than”). This means any number smaller than 77 is a solution to the inequality { n │ n < 77} This is called “set-builder notation.” It would be read as “n such that n is less than 77.”

4. Example C k – 4 > 10 k – 4 + 4 > 10 + 4 k > 14 Adding the same number to each side of an inequality does not change the direction of the inequality. {k │ k > 14 } Set builder notation is always placed inside of braces.

5. Graphing on the Number Line (A Quick Review) Great than or equal to (≥) and less than or equal to ( ≤) uses a filled in (or closed) circle then shade the line in the same direction the symbol is pointing. Great than (>) and less than ( <) uses an unshaded (or open) circle then shade the line in the same direction the symbol is pointing.

6. 12 + 9 y – 9 + 9 y 21 y ≥ ≤ ≥ Add y │y ≤ 21

7. Subtraction Property of Inequality – If any number is ___________ from ________ side of a true inequality, the resulting inequality is also _______. subtracted each true subtract q + 23 - 2314 - 23 < q < -9 {q │q < –9}

8. x – 2 < 8 x – 2 + 2 < 8 + 2 x < 10 The symmetric property does not work for inequalities, so if you “turn the inequality around” you have to change the sign, too. { x │ x < 10} m + 15 – 15 ≤ 13 - 15 m ≤ –2 { m │ m ≤ –2 }

9. Variables on Both Sides Example H 12n – 4 ≤ 13n 12n –12n – 4 ≤ 13n –12n – 4 ≤ n n ≥ – 4 { n │ n ≥ – 4}

10. Example I 3p – 6 ≥ 4p 3p – 3p – 6 ≥ 4p – 3p – 6 ≥ p p ≤ – 6 { p │ p ≤ – 6 }

11. Example J 5x + 4 > 4x + 10 5x + 4 – 4x > 4x – 4x + 10 x + 4 > 10 x + 4 – 4 > 10 – 4 x > 6 {x │ x > 6 }

12. Ex. K Seven time a number is greater than 6 times that number minus two. 7x > 6x – 2 7x – 6x > 6x – 6x – 2 x > – 2 Ex. L Three times a number is less than two times that number plus 5. 3x < 2x + 5 3x – 2x < 2x – 2x + 5 x < 5