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2. Lesson Menu Objectives Vocabulary Example 1 Example 2 Example 3 Example 4 Quick Quiz

3. Objectives To express a balance puzzle as an algebraic equation To represent an equation as a balance puzzle To solve simple word problems by writing and solving equations To solve equations without using the balance puzzle model

4. Vocabulary solution set inequality

5. Example 1 Solve x + 4 = 5. Method 1Use models. Model the equation. Remove 4 counters from each side. Solving Equations Using Algebra Tiles

6. Example 1 Method 2 Use symbols. Answer: The solution is 1. 5 – 4 = 1 x + 4 = 5Write the equation. x = 1 – 4 = – 4Subtract 4 from each side to “undo” the addition of 4 on the left. Check 1 + 4 = 5

7. 1.A 2.B 3.C 4.D Example 1 Solve x + 7 = 13. A.x = –20 B.x = –6 C.x = 6 D.x = 20

8. Example 2 PENNSYLVANIA The width of Pennsylvania (from north to south) is 280 miles. This is 120 miles more than the length of the state (from east to west). Write and solve an addition equation to find the length of Pennsylvania. Wordslength plus 120 miles is 280 miles VariableLet x represent the length of Pennsylvania. Equationx + 120 = 280

9. Example 2 Answer: So, the length of Pennsylvania is 160 miles. x + 120=280Write the equation. x= 160280 – 120 = 160 – 120=–120Subtract 120 from each side.

10. 1.A 2.B 3.C 4.D Example 2 INTERNET Steve was on the Internet for 40 minutes last night. This was 15 more minutes than Beth spent on the Internet the same night. Write and solve an addition equation to find the amount of time Beth spent on the Internet last night. A.15 – t = 40; 20 minutes B.15 + t = 40; 25 minutes C.40 + t = 15; 25 minutes D.40 – t = 15; 55 minutes

11. Example 3 Solve x – 5 = –1. Check your solution. Answer: The solution is 4. Simplify. x – 5 = –1 x = 4 + 5 = + 5 Add 5 to each side. Check x – 5 = –1 –1 = –1 Write the equation. 4 – 5 = –1 ?

12. 1.A 2.B 3.C 4.D Example 3 Solve d – 8 = –5. Check your solution. A.–13 B.–3 C.3 D.13

13. Example 4 For the given value, state whether the inequality is true or false. x – 4 < 6; x = 0 Answer: Since –4 is less than 6, –4 < 6 is true. –4 < 6Simplify 0 – 4 < 6Replace x with 0. ? x – 4 < 6Write the inequality.

14. 1.A 2.B Example 4 For the given value, state whether the inequality is true or false. x – 5 < 8; x = 16 A.true B.false

15. 1.A 2.B 3.C 4.D Quick Quiz 1 In a balance puzzle, 4 bags and 2 blocks balance 2 bags and 10 blocks. Select the equation describing the balance. A.4b + 2 = 2b + 10 B.4 + 2 = 2b + 10 C.4b + 2 = 4 + 10 D.6b = 12

16. 1.A 2.B 3.C 4.D Quick Quiz 2 Solve the inequality 3s – 2 > 19 by doing the same thing to both sides. A.s > 8.3 B.s > 7 C.s > 5.6 D.s > 8

17. 1.A 2.B 3.C 4.D Quick Quiz 3A A. Amelia is selecting a new printer for the school newspaper staff. Printer A costs $500. It costs $0.07 for each page printed. Printer B costs $800. It costs $0.05 for each page printed. Write an equation you could solve to find the number of pages at which the total cost for each printer is the same. The total cost of the printer is the purchase cost and the cost to print each page. A.500 + 0.07 = 800 + 0.05 B.500 + 0.07x = 800 + 0.05 C.500 + 0.07x = 800 + 0.05x D.500x + 0.07 = 800x + 0.05

18. 1.A 2.B 3.C 4.D Quick Quiz 3B B. Amelia is selecting a new printer for the school newspaper staff. Printer A costs $500. It costs $0.07 for each page printed. Printer B costs $800. It costs $0.05 for each page printed. Solve the equation in 3A by doing the same thing to both sides. A.x = 4,000 B.x = 40,000 C.x = 13,000 D.x = 15,000

19. 1.A 2.B 3.C 4.D Quick Quiz 3C A. B. C.3 D.2

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21. Resources Image Bank Math Tools Multilingual e-Glossary Solving Equations Using Algebra Tiles Spreadsheets Solving EquationsTwo-Step Equations

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