<ul> <li>Slide 1</li> <li>1.4 Solving Absolute Value Equations</li> <li>Slide 2</li> <li>Absolute Value</li> <li>Slide 3</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only</li> <li>Slide 4</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only</li> <li>Slide 5</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs)</li> <li>Slide 6</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5|</li> <li>Slide 7</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5</li> <li>Slide 8</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| =</li> <li>Slide 9</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1</li> <li>Slide 10</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3</li> <li>Slide 11</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=</li> <li>Slide 12</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4</li> <li>Slide 13</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 +</li> <li>Slide 14</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5</li> <li>Slide 15</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3)</li> <li>Slide 16</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7|</li> <li>Slide 17</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4</li> <li>Slide 18</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 +</li> <li>Slide 19</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15</li> <li>Slide 20</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7|</li> <li>Slide 21</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4</li> <li>Slide 22</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 +</li> <li>Slide 23</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22|</li> <li>Slide 24</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4</li> <li>Slide 25</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 +</li> <li>Slide 26</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22</li> <li>Slide 27</li> <li>1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22 = 23.4</li> <li>Slide 28</li> <li>Example 2</li> <li>Slide 29</li> <li>Example 2 Solve |x 18| = 5.</li> <li>Slide 30</li> <li>|x 18| = 5</li> <li>Slide 31</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5</li> <li>Slide 32</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5</li> <li>Slide 33</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5</li> <li>Slide 34</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5</li> <li>Slide 35</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5</li> <li>Slide 36</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5</li> <li>Slide 37</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18</li> <li>Slide 38</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 x = 23</li> <li>Slide 39</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23</li> <li>Slide 40</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13</li> <li>Slide 41</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3</li> <li>Slide 42</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0.</li> <li>Slide 43</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0</li> <li>Slide 44</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9</li> <li>Slide 45</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9</li> <li>Slide 46</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note:</li> <li>Slide 47</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!</li> <li>Slide 48</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!</li> <li>Slide 49</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!</li> <li>Slide 50</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!</li> <li>Slide 51</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!</li> <li>Slide 52</li> <li>Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number! x =</li> <li>Slide 53</li> <li>Example 4</li> <li>Slide 54</li> <li>Example 4 Solve |x + 6| = 3x 2.</li> <li>Slide 55</li> <li>|x + 6| = 3x 2</li> <li>Slide 56</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2</li> <li>Slide 57</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2</li> <li>Slide 58</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2</li> <li>Slide 59</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2)</li> <li>Slide 60</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2)</li> <li>Slide 61</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6</li> <li>Slide 62</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 =</li> <li>Slide 63</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x</li> <li>Slide 64</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x</li> <li>Slide 65</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)</li> <li>Slide 66</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2</li> <li>Slide 67</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6</li> <li>Slide 68</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x</li> <li>Slide 69</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2</li> <li>Slide 70</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x</li> <li>Slide 71</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2</li> <li>Slide 72</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6</li> <li>Slide 73</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x</li> <li>Slide 74</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8</li> <li>Slide 75</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2</li> <li>Slide 76</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 77</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 78</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 79</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 80</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 81</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -8 -2 -2 x = 4</li> <li>Slide 82</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 x = 4</li> <li>Slide 83</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4</li> <li>Slide 84</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> <li>Slide 85</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> <li>Slide 86</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> <li>Slide 87</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> <li>Slide 88</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> <li>Slide 89</li> <li>Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1</li> </ul>