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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Equations, Inequalities and Problem Solving
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22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The sum of the angles of a triangle is 180°. If one angle of a triangle measures x° and a second angle measures (2x+7)°, express the measure of the third angle in terms of x. Simplify the expression. 2. A quadrilateral is a four-sided figure whose angle sum is 360°. If one angle measures x°, another 3x°, and another 5x°, express the measure of the fourth angle in terms of x. Simplify the expression. Hint: DRAW THE PICTURE!!
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33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The sum of the angles of a triangle is 180°. If one angle of a triangle measures x° and a second angle measures (2x+7)°, express the measure of the third angle in terms of x. Simplify the expression. x° (2x+7)° ?°
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44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. The sum of the angles of a triangle is 180°. If one angle of a triangle measures x° and a second angle measures (2x+7)°, express the measure of the third angle in terms of x. Simplify the expression. x° (2x+7)° ?° ?° = 180° - x° - (2x+7)° = (-3x+173)°
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55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 2. A quadrilateral is a four-sided figure whose angle sum is 360°. If one angle measures x°, another 3x°, and another 5x°, express the measure of the fourth angle in terms of x. Simplify the expression. x° ?° 5x° 3x°
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66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 2. A quadrilateral is a four-sided figure whose angle sum is 360°. If one angle measures x°, another 3x°, and another 5x°, express the measure of the fourth angle in terms of x. Simplify the expression. x° ?° 5x° 3x° ?° = 360° - x° - 3x° - 5x° = (-9x+360)°
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 2.3 The Multiplication Property of Equality
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88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives: Use the multiplication property of equality to solve linear equations Write work phrases as algebraic expressions
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99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiplication Property of Equality Let a, b, and c represent numbers and let c ≠ 0. Then, a = ba = b and a · c = b · cand are equivalentare equivalent equations.equations.
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10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1
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11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1
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12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1
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13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1
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14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 A number divided by itself is one!
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15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one!
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22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one! True Statement!
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23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve –4x = 16 for x. Check: Example 1 1 A number divided by itself is one! ✔ True Statement!
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24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2
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25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2
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26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2
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27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2 The product of reciprocals is one!
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28 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2 The product of reciprocals is one!
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29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2 The product of reciprocals is one! Simplify
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30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Example 2 The product of reciprocals is one! Simplify
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31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3
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32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3
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33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3
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34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3 A number divided by itself is one!
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35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3 A number divided by itself is one!
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36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: –1.2x = –36 Example 3 A number divided by itself is one!
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37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve:
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38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve:
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39 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve:
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40 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve:
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41 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve:
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42 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve: The product of reciprocals is one!
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43 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 4 Simplify both sides. Multiply both sides by 7. Solve: The product of reciprocals is one!
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44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5
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45 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5
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46 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5
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47 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5
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48 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5 A number divided by itself is one!
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49 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 4x – 8x = 16 Example 5 A number divided by itself is one!
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50 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26
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51 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26
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52 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides!
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53 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides!
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54 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Simplify
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55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Simplify
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56 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Simplify Divide on both sides!
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57 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Divide on both sides! Simplify
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58 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Divide on both sides! Simplify
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59 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 6 3z – 1 = 26 3z = 27 z = 9 3z – 1 + 1 = 26 + 1 Solve: 3z – 1 = 26 Add to both sides! Divide on both sides! Simplify
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60 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7
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61 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify
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62 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify
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63 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides!
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64 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides!
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65 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify
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66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify
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67 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify Divide on both sides!
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68 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify Divide on both sides!
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69 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify Divide on both sides! Simplify
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70 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 12x + 30 + 8x – 6 = 10 20x + 24 = 10 20x = – 14 20x + 24 + ( – 24) = 10 + ( – 24) Solve: Example 7 Simplify Add to both sides! Simplify Divide on both sides! Simplify
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71 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8
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72 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute
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73 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute
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74 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify
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75 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify
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76 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides!
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77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides!
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78 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify
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79 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify
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80 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify Divide on both sides!
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81 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify Divide on both sides!
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82 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify Divide on both sides! Simplify
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83 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 – 15 = 6 – 15 10x + 15 = 6 10x = –9 Example 8 Distribute Simplify Add to both sides! Simplify Divide on both sides! Simplify
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84 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Recall: Integers are the whole steps from -∞ to ∞, and consecutive means one right after another. Consecutive Integers Consecutive integers If n is the first integer, then: n+1 is the second, n+2 is the third, n+3 is the fourth, etc…
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85 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Recall: Integers are the whole steps from -∞ to ∞, and consecutive means one right after another. Consecutive Integers Consecutive even integers If n is the first integer, then: n+2 is the second, n+4 is the third, n+6 is the fourth, etc…
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86 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Recall: Integers are the whole steps from -∞ to ∞, and consecutive means one right after another. Consecutive Integers Consecutive odd integers If n is the first integer, then: n+2 is the second, n+4 is the third, n+6 is the fourth, etc…
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87 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9
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88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9
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89 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second
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90 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum
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91 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum 1 st + 2 nd is the sum
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92 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum 1 st + 2 nd is the sum x + (x + 1)
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93 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum 1 st + 2 nd is the sum x + (x + 1) Simplify
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94 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum 1 st + 2 nd is the sum x + (x + 1) x + x + 1 Simplify
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95 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If x is the first of two consecutive integers, express the sum of the first and the second integer in terms of x. Simplify if possible. Example 9 x is the first consecutive integer no even or odd, so x + 1 is the second express the sum 1 st + 2 nd is the sum x + (x + 1) x + x + 1 Simplify 2x + 1
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96 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Closure: 1. What is the Multiplication Property of Equality? 2. What should you do to both sides of an equation?
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97 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass 5(3x – 1) + 2 = 12x + 6 Step 1_________________ Step 2_________________ Step 3_________________ Step 4_________________ Step 5_________________ Solve the equation for x. Describe your process for each step.
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98 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3
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99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3 Distribute
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100 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3 Distribute Simplify or Combine like terms
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101 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3 Distribute Simplify or Combine like terms Add same on both sides
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102 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3 Distribute Simplify or Combine like terms Add same on both sides
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103 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass Solve the equation for x. Describe your process for each step. 5(3x – 1) + 2 = 12x + 6 15x – 5 + 2 = 12x + 6 _________________ 15x – 3 = 12x + 6 _________________ 3x – 3 = 6 _________________ 3x = 9 _________________ 3x/3 = 9/3 _________________ x=3 Distribute Simplify or Combine like terms Add same on both sides Divide on both sides Add same on both sides
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