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

3. Objectives To solve equations by adding, multiplying, or dividing both sides by the same quantity To describe variable quantities that appear in typical word problems, including those that refer to signed numbers To add and subtract parenthetical expressions

4. Vocabulary conjecture

5. Example 1 Solve 5x + 12 = 2x. Check your solution. 5x + 12=2xWrite the equation. 5x – 5x + 12=2x – 5xSubtract 5x from each side. 12=–3xSimplify. –4=xMentally divide each side by –3. Subtract 5x from the left side of the equation to isolate the variable. Subtract 5x from the right side of the equation to keep it balanced

6. Example 1 To check your solution, replace x with –4 in the original equation. Check 5x + 12=2xWrite the equation. Answer: The solution is –4. 5(–4) + 12=2(–4)Replace x with –4. ? –20 + 12=–8Simplify. ? –8=–8This statement is true. Solving Equations

7. 1.A 2.B 3.C 4.D Example 1 Solve 7x = 5x + 6. Check your solution. A.–3 B. C.3 D.21

8. Example 2 A. Solve 3h = 5(h – 2). Check your solution. 3h=5(h – 2) Write the equation. 3h=5(h) – 5(2)Use the Distributive Property. 3h=5h – 10Simplify. 3h – 5h=5h – 5h – 10Subtract 5h from each side. –2h=–10Simplify. Divide each side by –2.

9. Example 2 h =5Simplify. Check 3h=5(h – 2)Write the equation. Answer: The solution is 5. 3(5)=5(5 – 2)Replace h with 5. ? ? 15=5(3)Simplify. 15=15This statement is true. Two-Step Equations

10. Example 2 B. Solve 6(b – 2) = 3(b + 8.5). Check your solution. 6(b – 2)=3(b + 8.5) Write the equation. 6b – 12=3b + 25.5Use the Distributive Property. 6b – 3b – 12 = 3b – 3b + 25.5Subtract 3b from each side. 3b – 12=25.5Simplify. 3b – 12 + 12=25.5 + 12Add 12 to each side. 3b=37.5Simplify. Divide each side by 3.

11. Example 2 b =12.5Simplify. Answer: The solution is 12.5.

12. 1.A 2.B 3.C 4.D Example 2 A. Solve 4t = 7(t – 3). Check your solution. A.–7 B.1 C. D.7

13. 1.A 2.B 3.C 4.D Example 2 B. Solve 3(p + 5) = 6(p – 2). Check your solution. A.9 B.8 C. D.

14. Example 3 GEOMETRY The perimeter of a rectangle is 36 inches. Find the dimensions if the length is 2 inches greater than three times the width. Words2 times the length + 2 times the width = perimeter VariableLet w = the width. Let 3w + 2 = the length. Equation2(3w + 2) + 2w = 36 3w + 2 w

15. Example 3 2(3w + 2) + 2w = 36Write the equation. 6w + 4 + 2w=36Use the Distributive Property. 8w + 4=36Simplify. 8w + 4 – 4=36 – 4Subtract 4 from each side. 8w=32Simplify. w=4Mentally divide each side by 8. Evaluate 3w + 2 to find the length. 3(4) + 2 = 12 + 2 or 14Replace w with 4. Answer: The width is 4 inches. The length is 14 inches.

16. 1.A 2.B 3.C 4.D Example 3 GEOMETRY The perimeter of a rectangle is 26 feet. Find the dimensions if the length is 2 feet less than twice the width. A. B. C.width = 5 ft; length = 8 ft D.width = 11 ft; length = 24 ft

17. 1.A 2.B 3.C 4.D Quick Quiz 1A A. An airplane climbs at a rate of n feet per minute. The same airplane glides down to Earth without power at a rate of q feet per minute. Select an expression describing the change in altitude if it first climbs for 5 minutes and then glides for 2 minutes. A.5n + 2q B.5n – 2q C.5n – q D.n + 5 – 2q

18. 1.A 2.B 3.C 4.D Quick Quiz 1B B. The same airplane starts at 5,000 feet above sea level. It climbs for 10 minutes and then glides to earth for 8 minutes. Select an expression that describes the glider’s altitude above sea level at that point. A.5,000 + n – q B.5,000 – 10n + 8q C.5,000 + 10n – 8q D.5,000 + 10 – 8

19. 1.A 2.B 3.C 4.D Quick Quiz 2A A. Select the correct expression without parentheses for 2 – 3(4 – 6). Then evaluate the expression. A.2 – 12 + 18; 8 B.2 – 12 – 24; –34 C.8 – 12 – 18; –22 D.2 + 18 – 24; –4

20. 1.A 2.B 3.C 4.D Quick Quiz 2B B. Select the correct expression without parentheses for – 7 + (–2 + 3). Then evaluate the expression. A.–7 – 2 + 3; –6 B.–7 + 14 – 21; –14 C.–7 – 14 + 21; 0 D.–7 + 2 – 3; –8

21. 1.A 2.B 3.C 4.D Quick Quiz 3 Simplify 5n – 3(2 – 6n). A.23n – 6 B.23n + 6 C.13n – 6 D.13n + 6

22. 1.A 2.B 3.C 4.D Quick Quiz 4 Solve the equation 3g + 2(6 – g) = 4 + 5(g + 1). A. B.g = 3 C. D.g = 4

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

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