a carpenter cuts boards that are 2 meters long. It is acceptable for the length to differ from this value by at most 0.05 meters.

Question

write and solve an absolute value inequality to find the range of acceptable lengths 

 

Answer 1

The difference between the ideal length (2 meters) and the actual length (L) needs to be less than or equal to 0.05 meters.  We know that subtraction is the mathematical operation used to find the difference between two numbers.  Since L can be greater than (positive difference), less than (negative difference) two meters, or equal to the ideal length, we need to use an absolute value for our inequality.

 

|Actual Length - Ideal Length| ≤ Acceptable Difference

 

or

 

|L - 2 meters| ≤ 0.05 meters

 

The absolute value of the difference between the actual length and the ideal 2 meter length of the boards the carpenter cuts must be less than or equal to 0.05 meters.

Answer 2

If -B ≤ A ≤ B, then lAl ≤ B

 

Let x = length of board

 

Then 2 - 0.05 ≤ x ≤ 2 + 0.05

 

So, -0.05 ≤ x - 2 ≤ 0.05

 

Therefore, l x - 2 l ≤ 0.05