1. Inequalities

2. Objective:
Solve inequalities by using the addition, subtraction, multiplication, and division Properties of Inequality
Standard:
7.EE.4
7.EE.4.b

3. INEQUALITIES

4. Solving Inequalities by Addition and Subtraction
You can solve inequalities by using the Addition Property of Inequalities and the Subtraction Property of Inequalities. When you add or subtract the same number from each side of an inequality, the inequality remains true.
Symbols For all numbers a, b, and c,
1. If a > b, then a + c > b + c and a – c > b – c.
2. If a < b, then a + c < b + c and a – c < b – c.
Examples 2 < > 3
5 < > –1
look at the table on page 498 for ways to read inequalities

5. INEQUALITIES
solve for x and check your solution
ex: x + 3 > 10

6. Graphing Inequalities on a number line
When graphing the solution to an inequality, use an open dot to show > or <. Use a closed dot to indicate the solution is ≥ or ≤.
Solve. Graph the solution set on a number line.
a + ½ < 2

7. I DO, WE DO, YOU DO h + 4 > 4 x - 6 ≤ 4 m + 5 ≥ -1
Solve each inequality. Graph the solution set on a number line.
h + 4 > 4
x - 6 ≤ 4
m + 5 ≥ -1

8. On Your Own

9. On Your Own

10. Multiplication and Division Properties of Inequalities (Positive Numbers)
The Multiplication Property of Inequalities and the Division Property of Inequalities states that an inequality remains true when you multiply or divide each side of an inequality by a positive number.
Symbols For all numbers a, b, and c, where c > 0.
1. If a > b, then ac > bc and a/c > b/c.
2. If a < b, then ac < bc and a/c < b/c.
These properties are also true for a ≥ b and a ≤ b
example: 8x ≤ 40
d/2 > 7

11. Multiplication and Division Properties of Inequalities (Negative Numbers)
When you multiply or divide each side on an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
Symbols For all numbers a, b, and c, where c < 0.
1. If a > b, then ac < bc and a/c < b/c.
2. If a < b, then ac > bc and a/c > b/c.
These properties are also true for a ≥ b and a ≤ b
example: -2g < 10
x/-3 ≤ 4

12. I DO, WE DO, YOU DO 4x < 40 k/-2 < 9 6 ≥ x/7
Solve each inequality. Graph the solution set on a number line.
4x < 40
k/-2 < 9
6 ≥ x/7

13. GOTCHA! DO IT AGAIN -3n ≤ -22 t/-4 < -11 -8 < y/5
Solve each inequality. Graph the solution set on a number line.
-3n ≤ -22
t/-4 < -11
-8 < y/5

14. LESSON KEY CONCEPT Multiplying and Dividing Inequalities
When you multiply or divide each side of an inequality by a positive number, the direction of the inequality symbol remains unchanged.
When you multiply or divide each side of an inequality by a negative number, the direction of the inequality symbol must be reversed.

15. DO NOW
ON YOUR OWN
EVEN NUMBERS PAGE 509 AND 510
FOR HOMEWORK
ODD NUMBER PAGE 509 AND 510

16. Objective: State Standard: model two-step inequalities
solve two-step inequalities
represent the solution on the number line
State Standard:
7.EE.4
7.EE.4.b

17. SOLVE A TWO-STEP INEQUALITY
A two-step inequality is an inequality that contains two operations. To solve a two-step inequality, use inverse operations to undo each operation in revere of the order of operations.
Example: 3x + 4 ≥ 16
Graph the solution set on a number line.

18. I DO, WE DO, YOU DO 5 + 4x < 33 2x + 8 > 24 6x + 14 ≥ 20
Solve. Graph the solution set on a number line.
5 + 4x < 33
2x + 8 > 24
6x + 14 ≥ 20

19. I DO, WE DO, YOU DO Some more
Solve. Graph the solution set on a number line.
7 - 2x > 11
x/2 - 5 < -8
x/2 + 9 ≥ 5

20. WE DO - pg 516 together YOU DO - PG 517 & 518 evens with partner