1. Algebra 2 Lesson 1-3 (Page 18) ALGEBRA 2 LESSON 1-3 Solving Equations 1-1

2. To solve equations. ALGEBRA 2 LESSON 1-3 Solving Equations 1-1

3. New Vocabulary ALGEBRA 2 LESSON 1-3 Solving Equations 1-1 A number that makes the equation true is a solution of the equation.

4. Properties of Equality (Page 18) ALGEBRA 2 LESSON 1-3 Solving Equations 1-1

5. Solving Equations ALGEBRA 2 LESSON 1-3 Solve 7x + 3 = 2x – 12. 7x + 3 = 2x – 12 5x + 3 = –12Subtract 2x from each side. 5x = –15Subtract 3 from each side. x = –3Divide each side by 5. 1-3 Check:7x + 3 = 2x – 12 7(–3) + 3 2(–3) – 12 –18 = –18

6. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

7. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

8. Solving Equations ALGEBRA 2 LESSON 1-3 Solve 4(m + 9) = –3(m – 4). 4(m + 9) = –3(m – 4) 4m + 36 = –3m + 12Distributive Property 7m + 36 = 12Add 3m to each side. 7m = –24Subtract 36 from each side. 1-3 m = –Divide each side by 7. 24 7

9. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

10. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

11. Solving Equations ALGEBRA 2 LESSON 1-3 The formula for the surface area of a rectangular prism units long, w units wide, and h units high is A = 2( w + h + wh). Solve the formula for w. A = 2( w + h + wh) A = 2 w + 2 h + 2whDistributive Property A – 2 h = 2 w + 2whSubtract 2 h from each side. A – 2 h = (2 + 2h)wDistributive Property 1-3 = wDivide both sides by 2 + 2h. A – 2 h 2 + 2h

12. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

13. Solving Equations ALGEBRA 2 LESSON 1-3 Solve + 8 = b for x. Find any restrictions on a and b. xaxa x + 8a = abSimplify. 1-3 + 8 = b xaxa a ( ) + a(8) = abMultiply each side by the least common denominator (LCD), a. xaxa x = ab – 8aSubtract 8a from each side. =/ The denominator cannot be zero, so a 0.

14. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

15. Solving Equations ALGEBRA 2 LESSON 1-3 Try this one on your own. Check your answer. 1-3

16. To solve problems by writing equations. ALGEBRA 2 LESSON 1-3 Solving Equations 1-1

17. Solving Equations ALGEBRA 2 LESSON 1-3 Adrian will use part of a garage wall as one of the long sides of a rectangular rabbit pen. He wants the pen to be 3 times as long as it is wide. He plans to use 68 ft of fencing. Find the dimensions of the pen. Relate:2 width + length = perimeter Define:Let w = the width. Then 3w = the length. Write:2 w + 3w = 68 1-3

18. Solving Equations ALGEBRA 2 LESSON 1-3 (continued) 5w = 68Add. Check: Is the answer reasonable? Since the dimensions are about 14 ft by 41 ft and 14 + 14 + 41 = 69, the perimeter is about 69 ft. The answer is reasonable. 1-3 w = 13Divide each side by 5. 3535 3w = 40Find the length. 4545 3535 The width is 13 ft and the length is 40 ft. 4545

19. Solving Equations ALGEBRA 2 LESSON 1-3 The sides of a quadrilateral are in the ratio 1 : 2 : 3 : 6. The perimeter is 138 cm. Find the lengths of the sides. Relate:Perimeter equals the sum of the lengths of the four sides. Define:Let x = the length of the shortest side. Then 2x = the length of the second side. Then 3x = the length of the third side. Then 6x = the length of the fourth side. 1-3

20. Solving Equations ALGEBRA 2 LESSON 1-3 (continued) Write:138= x + 2x + 3x + 6x 138= 12xCombine like terms. 11.5= x 2x= 2(11.5) 3x = 3(11.5) 6x = 6(11.5) Find the length of = 23 = 34.5 = 69 each side. Check: Is the answer reasonable? Since 12 + 23 + 35 + 69 = 139, the answer is reasonable. The lengths of the sides are 11.5 cm, 23 cm, 34.5 cm, and 69 cm. 1-3

21. Solving Equations ALGEBRA 2 LESSON 1-3 A plane takes off from an airport and flies east at a speed of 350 mi/h. Thirty-five minutes later, a second plane takes off from the same airport and flies east at a higher altitude at a speed of 400 mi/h. How long does it take the second plane to overtake the first plane? 1-3 Relate:distance first plane travels = distance second plane travels. Define:Let t = the time in hours for the second plane. Then t + = the time in hours for the first plane. 35 60 Write:400t= 350 ( t + ) 7 12 400t= 350t +Distributive Property 1225 6

22. Solving Equations ALGEBRA 2 LESSON 1-3 (continued) 50t= Solve for t. 1225 6 1-3 t= 4 h or about 4 h 5 min 1 12 Check: Is the answer reasonable? In 4 h, the second plane travels 1600 mi. In 4 h, the first plane travels about 1600 mi. The answer is reasonable. 2323