LINEAR INEQUALITIES

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LINEAR INEQUALITIES
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Checking Solutions

• An ordered pair (x,y) is a solution if it makes
  the inequality true.
• Are the following solutions to
• 3x 2y 2
• (0,0) (2,-1) (0,2)

3(0) 2(2) 2 4 2 Is a solution
3(2) 2(-1) 2 4 2 Is a solution
3(0) 2(0) 2 0 2 Not a solution
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• If the arrow points to the
• Right it is gReater than..
• ------gt
• If the arrow points to the
• Left it is Less than..
• lt------

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Steps to Graphing Linear Inequalities

• 1. Change the inequality into slope-intercept
  form,
• y mx b.
• 2. If gt or lt then the line should be dashed.
• If gt or lt then the line should be solid.
• 3. If y gt mxb or y gt mxb, shade the half plane
  
• ABOVE (gReater) the line.
• If y lt mxb or y lt mxb, shade the half plane
• below (Less) the line.

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To sketch the graph of a linear inequality

• Sketch the line given by the corresponding
  equation (solid if or , dashed if lt or gt).
  This line separates the coordinate plane into 2
  half-planes. In one half-plane all of
  the points are solutions of the inequality.
  In the other half-plane - no point is a
  solution
• You can decide whether the points in an entire
  half-plane satisfy the inequality by testing ONE
  point in the half-plane.
• Shade the half-plane that has the solutions to
  the inequality.

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The graph of an inequality is the graph of all
the solutions of the inequality

• 3x 2y 2
• y -3/2x 1 (put into slope intercept to
  graph easier)
• Graph the line that is the boundary of 2 half
  planes
• Before you connect the dots check to see if the
  line should be solid or dashed
• solid if or
• dashed if lt or gt

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Example
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Example
STEP 2
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Example
STEP 1
STEP 2
STEP 3
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ASSIGNMENT

• GET A BOOK
• TURN TO PAGE 833
• 18-19, 21-24..only 6 problemsjeeze /
• TURN IN TO THE BASKET WHEN COMPLETE.