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2.4 – Solving Equations with the Variable on Each Side.

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Presentation on theme: "2.4 – Solving Equations with the Variable on Each Side."— Presentation transcript:

1 2.4 – Solving Equations with the Variable on Each Side

2 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21

3 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21

4 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p)

5 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p)

6 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) +

7 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) +

8 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8)

9 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8)

10 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21

11 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p

12 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56

13 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21

14 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21

15 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21

16 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56

17 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56

18 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56

19 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56

20 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77

21 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77

22 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77 -7 -7

23 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77 -7 -7

24 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77 -7 -7 p = -11

25 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77 -7 -7 p = -11 Ex. 2 -4(p - 5) = 12

26 Note: REVERSE Order of Operations! Ex. 1 -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p + 0 = 77 -7p = 77 -7 -7 p = -11 Ex. 2 -4(p - 5) = 12 -4(p) – -4(5) = 12 -4p + 20 = 12 - 20 -20 -4p + 0 = -8 -4p = -8 -4 -4 p = 2

27 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1)

28 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1)

29 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5

30 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5

31 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k

32 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k

33 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5

34 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14

35 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14

36 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5

37 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5

38 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5

39 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k = 19

40 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k = 19 Ex. 2 2(b – 3) = 3(b – 1)

41 REMEMBER: REVERSE Order of Operations! Ex. 1 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k = 19 Ex. 2 2(b – 3) = 3(b – 1) 2(b)–2(3) = 3(b)–3(1) 2b – 6 = 3b – 3 -3b -3b -b – 6 = -3 + 6 +6 -b = 3 -1 -1 b = -3

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