Solving Inequalities

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Solving Inequalities

• Chapter 2.7

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Linear Inequalities

• Graph the indicated line
• Solid line lt, gt
• Dotted line lt, gt
• Choose a point not on the line to test
• If point satisfies inequality, shade region
  containing that point
• If point does not satisfy inequality, shade the
  other region

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Example Linear Inequality

• y gt 2x 1
• y-intercept at (0, 1)
• slope is 2
• Up 2, over 1
• Sketch solid line
• Test point (0, 0)
• y gt 2x -1
• 0 gt 2(0) 1
• 0 gt -1 true
• Shade this side

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Example Linear Inequality

• y lt -3/2x 2
• y-intercept at (0, 2)
• slope is -3/2
• Down 3, over 2
• Sketch dotted line
• Test point (0, 0)
• y lt -3/2x 2
• 0 lt -3/2(0) 2
• 0 lt 2 true
• Shade this side

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Example Linear Inequality

• y lt -2x
• y-intercept at (0, 0)
• slope is -2
• Down 2, over 1
• Sketch dotted line
• Test point (0, 1)
• y lt -2x
• 1 lt -2(0)
• 1 lt 0 not true
• Shade other side

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Absolute Value Inequalities

• Decide where to put the vertex of your graph
• Positive number inside move left x2
• Negative number inside move right x-3
• Positive number outside move up x1
• Negative number outside move down x-2
• Sketch your v-shape
• Test a point that is not on the graph
• If point satisfies inequality, shade region
  containing that point
• If point does not satisfy inequality, shade the
  other region

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Example Absolute Value Inequality

• y gt x 1
• Vertex does not move left or right
• Vertex moves 1 unit up
• Plot points 1 unit up in both directions to make
  ensure a nice shape
• Sketch dotted v-shape
• Test (0, 0)
• ygt x 1
• 0gt 0 1
• 0gt1 not true
• Shade other side

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Example Absolute Value Inequality

• y lt x-1 -2
• Vertex moves 1 unit right
• Vertex moves 2 units down
• Plot points 1 unit up in both directions
• Sketch solid v-shape
• Test (0, 0)
• y lt x - 1 - 2
• 0 lt 0 - 1 - 2
• 0 lt -1 - 2
• 0 lt 1 - 2
• 0 lt -1 not true
• Shade other side

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Assignment

• Graphing Inequalities worksheet
• Work on your own quietly
• Ill be around to help
• Finish for homework