Download Solving Inequalities

Solving Inequalities
Inequalities Are Everywhere
Defining
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
vary?
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
So:
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
class?
Computing Grades
Our grade in this class is the average of the
test scores. In math, how do we find an
average?
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
Then
G
68  82  87  89  x 326  x

5
5
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
326

x
80 
 90
5
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.