You have an after school job mowing lawns. The number of lawns that you would like to mow per week is 8. You have to mow at least 4 lawns each week and you

Question

can't now more than 12 lawns each week. If "m" represents the number of lawns that you mow each week, which of the following absolute value inequalities would represent the number of lawns you could possible mow in one week?

1. |m-8|<=12

2. |m-4|<=12

3. |m-8|<=4

4. |m-4|<=8

Answer 1

The number of lawns that you would like to mow per week is 8.

THIS IS THE IDEAL NUMBER

 

 

You have to mow at least 4 lawns each week

THIS IS THE MINIMUM NUMBER

 

 

and you can't now more than 12 lawns each week.

THIS IS THE MAXIMUM NUMBER

 

LET'S START WITH AN EXPRESSION WITH THE MINIMUM AND MAXIMUM:

 

4 ≤ m ≤ 12

 

in order to change this into a single absolute value inequality, m needs to be bounded by opposites; so, let's subtract 8 -the ideal number - from each piece

 

4 - 8 ≤ m - 8  ≤ 12 - 8   (simplify each piece)

 

-4 ≤ m - 8 ≤ 4   ( m is now bounded by opposites)

 

l m - 8 l ≤ 4