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      Algebra : Inequalities : Inequalities and regions

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      Inequalities and regions

      • Posted by sapayth
      • Categories Inequalities
      • Comments 0 comment
      a4-3-inequalities-and-regions

      Vertical regions

      Graphs can be used to represent inequalities by regions (region is the area where all points obey a given rule).

      For example, the region for x > 2 is represented by:

      ys-a-4-3-1

      In the graph, the area where the graph is x > 2 is shown above. In this area, all of the points would be more than 2.

      The line which intersects where  x = 2 is drawn with a dotted line.

      In the right region of the line x = 2, every point represents x > 2.

      In the left region of the line x = 2, every point represents x < 2.

      Horizontal regions

      The rules for horizontal regions will follow the rules for the vertical regions. Therefore the graph which represents y ≤ 3 is:

      ys-a-4-3-2

      In the graph, the area where the graph is y ≤ 3 is shown above. In this area, all of the points would be more than or equal to 3.

      The line which intersects where  y = 3 is drawn with a solid line.

      In the top region of the line y = 3, every point represents y > 3 and y = 3

      In the left region of the line y = 3, every point represents y < 3 and y = 3

      Horizontal and vertical regions combined

      When combining horizontal and vertical regions, the unwanted regions are shaded out. This enables the required area to be easily identified.

      ys-a-4-3-3

      In the graph above, the regions represent  –4 < x < –1 and –1 < y ≤ 3.

      The regions which are unshaded represent –4 < x < –1 and –1 < y ≤ 3.

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      Solving linear inequalities
      October 12, 2016

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      Inequalities

      • Representing inequalities on number lines
      • Solving linear inequalities
      • Inequalities and regions
      • Inequalities in two variables
      • Quadratic inequalities

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