Equations and Inequalities

1. Equations and Inequalities • Remember to think about your clue words! • Less than : Subtraction • Per : multiplication • More than : addition • No more than : < • No less than : > • More than : > • Less than : <

2. Equations and Inequalities • If you can set up an expression you can set up an equation, or inequality. • For example, • 73 – 14 = x is the same as 73 = x + 14 • All you have to do is use your inverse operations!

3. Equations and Inequalities • Mary’s CD player cost $113 less than her DVD player. Her CD player cost $78. How much was her DVD player?

4. Equations and Inequalities • Maria wants to pack and ship a total of 288 pens. If each box holds 12 pens, how many boxes are needed to ship the pens?

5. Equations and Inequalities • An airline lets you check no more than 65 pound so luggage. One suitcase weighs 37 pounds. How much can the other suitcase weigh?

6. Equations and Inequalities • A 1-ton truck has the ability to haul 1 ton, or 2000 pounds. At most, how many televisions sets can the truck carry if each TV set weighs 225lb?

7. Write an equation or inequality • Susan’s CD player cost $120 less than her DVD player. Her CD player cost $64. How much was her DVD player? • Jack wants to pack and ship 208 pens. If each box holds 8 pens

8. Getting Started • s + s + s + s + 4 • 4s + 4 • Are the two expressions equivalent? • How could you convince a student that the two expressions are equivalent?

9. Getting Started • 4s + 4 • 4(s + 1) • Are the two expressions equivalent? • How could you convince a student that the two expressions are equivalent?

10. Objective - To use the distributive property to simplify numerical and variable expressions. Distributive Property or Order of Operations Distributive Property It works! Why use the distributive property?

11. Simplify using the distributive property. 1) 4) 2) 5) 3) 6)

12. same same same Use the distributive property to write an equivalent expression. Then simplify both to show they have the same value. 1) 2) 3)

13. Simplify using the distributive property. 1) 4) 2) 5) 3) 6)

14. 4 5 2 Geometric Model for Distributive Property Two ways to find the area of the rectangle. As a whole As two parts

15. 4 5 2 same Geometric Model for Distributive Property Two ways to find the area of the rectangle. As a whole As two parts

16. Find the area of the rectangle in terms of x, y and z in two different ways. x y z As a whole As two parts

17. same Find the area of the rectangle in terms of x, y and z in two different ways. x y z As a whole As two parts

18. Use the distributive property to write an equivalent variable expression. Then simplify. 1) 4) 2) 5) 3) 6)

19. Use the distributive property to help simplify the following without a calculator. 1) 2)

20. Use the distributive property to help simplify the following without a calculator. 3) 4)

21. TOD • 5(x +y) • 33 + 8(x – 4) • 5(x + 3) + 4(y + 4)