1. Inequalities Are Everywhere
Solving Inequalities
Inequalities Are Everywhere

2. Defining
Middle-aged may be defined as being 40 or more and less than 60. How can I write this inequality?

3. 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?

4. Household Voltage

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?

6. 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?

7. Sales Commission
x 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:

8. Sales Commission The equation to use would be
The amount of money the car salesman could make would range from:
$53 to $145

9. 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?

10. Computing Grades
Our grade in this class is the average of the test scores. In math, how do we find an average?

11. Computing Grades Is the equation for finding my grade
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
Is the equation for finding my grade

12. Computing Grade
Now I set up an inequality to represent the range that I can make to get the B

13. 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

14. Markup of New Car

15. 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

16. 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.