Negative numbers are less than positive numbers. does this mean that the absolute value of a negative number must be less than the absolute value?

No

Step-by-step explanation:

No, its only sometimes . Lets take -7 and 4, the absolute value of -7 is greater then the absolute value of 4. Now take -3 and 4, the absolute vale of -3 is less than the absolute value of 4.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: