Graph Inequalities on a Number Line

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Graph Inequalities on a Number Line

• Integrated Math II
• Fortner

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Goals

• Determine if a number is a solution of an
  inequality.
• Graph the solution of an inequality on a number
  line.
• APPLICATIONS
• Business
• Government
• Sports
• Physics
• Geography

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Reading Math

• Words such as
• at least,
• at most
• less than
• maximum
• minimum
• Often indicate that an inequality will be used in
  solving a problem.

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What is a good  definition for Inequality? An
inequality is a statement that two expressions
are not equal
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• In this section we will help you understand how
  to graph inequalities on number lines. Many
  times you will have a statement such as x gt 5
  that needs to be graphed.  Because this is not an
  equation, it does not need to be graphed on the
  coordinate plane.  A number line does the job
  just fine! Some conventions that need to be
  remembered when graphing on a number line are
  explained below.
• 1.  An open circle is placed on the number line
  to show that the number denoted at the circle is
  not included in the solution set. 2.  A circle
  that is filled in is placed on the number line to
  show that the number denoted at the circle is
  included in the solution set.
• 1. Graph x lt 4 Solution The problem asks you
  to graph all numbers that are less than 4.

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Inequality Signs

• Read left to right
• a lt b    a is less than b
• a lt b   a is less than or equal to b
• a gt b     a is greater than b
• a gt b    a is greater than or equal to b

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Graphing Inequalitiesx lt c

• When x is less than a constant, you darken in the
  part of the number line that is to the left of
  the constant. 
• Also, because there is no equal line, we are not
  including where x is equal to the constant. 
• That means we are not including the endpoint. 
• One way to notate that is to use an open hole at
  that point.

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x gt c

• When x is greater than a constant, you darken in
  the part of the number line that is to the right
  of the constant. 
• Also, because there is no equal line, we are not
  including where x is equal to the constant. 
• That means we are not including the endpoint. 
• One way to notate that is to use an open hole at
  that point.

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x lt c

• When x is less than or equal to a constant, you
  darken in the part of the number line that is to
  the left of the constant. 
• Also, because there is an equal line, we are
  including where x is equal to the constant. 
• That means we are  including the endpoint. 
• One way to notate that is to use an closed hole
  at that point.

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x gt c

• When x is greater than or equal to a constant,
  you darken in the part of the number line that is
  to the right of the constant. 
• Also, because there is an equal line, we are
  including where x is equal to the constant. 
• That means we are including the endpoint. 
• One way to notate that is to use a closed hole at
  that point

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We can graph real numbers by representing them as
points on the number line. For example, we can
graph "2½ " on the number line
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• We can also graph inequalities on the number
  line.
• This graph represents the inequality x2 ½ .
• The dark line represents all the numbers that
  satisfy x2 ½ .
• If we pick any number on the dark line and plug
  it in for x, the inequality will be true.

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Inequalities and their Graphs
Terms you see and need to know to graph
inequalities correctly
lt less than
Notice open circles
gt greater than
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Terms you see and need to know to graph
inequalities correctly
less than or equal to
greater than or equal to
Notice colored in circles
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Lets work a few together
Notice when variable is on left side, sign
shows direction of solution
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Lets work a few together
Notice when variable is on left side, sign
shows direction of solution
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Color in circle
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Lets work a few together
Notice when variable is on left side, sign
shows direction of solution
Color in circle
-2
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Inequalities and their Graphs
Lets work a few together
Notice when variable is on left side, sign
shows direction of solution
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Try this one on your own
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On your Own
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Solve 2x lt 9

• If they had given me "2x 9", I would have
  divided the 2 from each side. I can do the same
  thing here

Then the solution is x lt 9/2
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When solving inequalities, if you multiply or
divide through by a negative, you must also flip
the inequality sign.

• To solve "2x lt 5",
• divide through by a negative ("2"), so
• need to flip the inequality

Then the solution is x gt 5/2