Solving Inequalities Solving Inequalities Inequalities Are Everywhere Defining Middle

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					Solving Inequalities
  Inequalities Are Everywhere
Middle-aged may be defined as being 40 or
 more and less than 60. How can I write
 this inequality?
         Household Voltage
In the United States, normal household
  voltage is 115 volts. However, it is not
  uncommon for actual voltage to differ from
  normal voltage by at most 5 volts. How
  can I express this inequality using
  Absolute Value?
Household Voltage

x115  5
         Sales Commission
A used car salesperson is paid a
  commission of $25 plus 40% of the selling
  price in excess of owner’s cost. The owner
  claims that used cars typically sell for at
  least owner’s cost plus $70 and at most
  owner’s cost plus $300. For each sale
  made, over what range can the
  salesperson expect the commission to
         Sales Commission
If we let C = the commission, we need to set
   up a combined inequality.

How do we solve a combined inequality?
How many equations are involved?
         Sales Commission
25 + 0.4x is the equation for the commission
  in excess of the owner’s cost

The least owner’s cost is $70
The most is $300

        Sales Commission
The equation to use would be

25.4(70) C  25 .4(300)
The amount of money the car salesman
could make would range from:

$53 to $145
          Computing Grades
In your English class, you have scores of 68,
  82, 87, and 89 on the first four of five tests.
  To get a grade of B, the average of the
  first five test scores must be great than or
  equal to 80 and less than 90.

What do you have to make to get a B in the
         Computing Grades
Our grade in this class is the average of the
 test scores. In math, how do we find an
          Computing Grades
So I know I have to make more than 80 and
  less than 90 to have a B. I need a variable for
  the unknown test grade.
Let x = the unknown test grade

  G      68  82  87  89  x 326  x
  Is the equation for finding my grade
           Computing Grade
Now I set up an inequality to represent the
 range that I can make to get the B

         80  326  x  90
       Markup of a New Car
The markup over dealer’s cost of a new car
 ranges from 12% to 18%. If the sticker
 price is $8800, over what range will the
 dealer’s cost vary?
Be careful. The cost is 100% + the markup.
So, the range would be
 Markup of New Car

8800      8800
     M 
1.12      1.18
    Absolute Value Inequalities
This is just a combined inequality.
 Remember, whenever you do an absolute
 value you do two different equations.

Distance is another name for absolute value.

So . . . .
   Absolute Value Inequalities
If the equation is < a number, the answer will
   be between the two solutions.

If the equation is > a number, the answer will
   be in opposite directions.

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