1. Solving Inequalities by Addition & Subtraction

2. Objective: 7.5.03 Essential Question: How can we use inverse operations to solve one step addition and subtraction ? How can we use inverse operations to solve one step addition and subtraction inequalities? Solving Inequalities by Addition & Subtraction

3. Review: Solving Inequalities by Addition & Subtraction < - is less than - is fewer than > - is more than - is greater than ≤ - is less than or equal to - is no more than ≥ - is greater than or equal to - is no less than

4. Real World: Brandi has $30 to spend on food and rides at a carnival. She has already spent $12 on food. Write an inequality and determine how much money she can spend on rides Inequality: m + 12 ≤ 30 m ≤ 18 Brandi can spend up to $18 on rides. Solving Inequalities by Addition & Subtraction

5. Example 1: Solve x + 3 > 9. x + 3 > 9 Solving Inequalities by Addition & Subtraction

6. Example 1: Solve x + 3 > 9. x + 3 > 9 – 3 – 3 x > 6 Solving Inequalities by Addition & Subtraction

7. Example 1: Solve x + 3 > 9. x + 3 > 9 – 3 – 3 x > 6 4 5 6 7 8 Solving Inequalities by Addition & Subtraction

8. Example 2: Solve x – 3 < 9. x – 3 < 9 Solving Inequalities by Addition & Subtraction

9. Example 2: Solve x – 3 < 9. x – 3 < 9 + 3 + 3 x < 12 Solving Inequalities by Addition & Subtraction

10. Example 2: Solve x – 3 < 9. x – 3 < 9 + 3 + 3 x < 12 10 11 12 13 14 Solving Inequalities by Addition & Subtraction

11. Example 3: Solve x + 3 ≥ – 9. x + 3 ≥ – 9 Solving Inequalities by Addition & Subtraction

12. Example 3: Solve x + 3 ≥ – 9. x + 3 ≥ – 9 – 3 – 3 x ≥ – 12 Solving Inequalities by Addition & Subtraction

13. Example 3: Solve x + 3 ≥ – 9. x + 3 ≥ – 9 – 3 – 3 x ≥ – 12 -14 -13 -12 -11 -10 Solving Inequalities by Addition & Subtraction

14. Example 4: Solve 12 + m ≤ 4. 12 + m ≤ 4 Solving Inequalities by Addition & Subtraction

15. Example 4: Solve 12 + m ≤ 4. 12 + m ≤ 4 – 12 – 12 m ≤ – 8 Solving Inequalities by Addition & Subtraction

16. Example 4: Solve 12 + m ≤ 4. 12 + m ≤ 4 – 12 – 12 m ≤ – 8 -10 -9 -8 -7 -6 Solving Inequalities by Addition & Subtraction

17. Independent Practice: Write an inequality and graph. 1. Two more than a number is less than eleven 2. Five less than a number is at least – 2 3. The difference between a number and ten is greater than 9 4. Four less than a number is less than 11 5. The sum of a number and seven is more than 1 Solving Inequalities by Addition & Subtraction

18. Independent Practice: Answers. 1. n < 91. 2. n ≥ 32. 3. n > 193. 4. n < 154. 5. n > – 65. 9 3 9 15 - 6 Solving Inequalities by Addition & Subtraction

19. Independent Practice: Solve each equation below. 1. y + 8 ≤ 12 2. d + 11 > 30 3. 4 + a ≥ – 1 4. 5 < 1 + k 5. h – 3 ≤ – 3 Solving Inequalities by Addition & Subtraction

20. Independent Practice: Answers. 1. y + 8 ≤ 12 1. 2. d + 11 > 30 2. 3. 4 + a ≥ – 1 3. 4. 5 < 1 + k 4. 5. h – 3 ≤ – 3 5. 4 19 - 5 4 0 Solving Inequalities by Addition & Subtraction

21. HOMEWORK Solving Inequalities by Addition & Subtraction