Question

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. Which inequality describes all the possible lengths (x), in inches, of the ribbons Jaime cut?

Answer 1

`|x-12|\leq 0.25`

`11.75\leq x\leq 12.25`

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:

`|x-12|\leq 0.25`

By the definition of absolute value function we will get,

`x-12\leq 0.25\text{ and} x-12\leq -0.25`

`x-12+12\leq 0.25+12\text{ and} x-12+12\leq -0.25+12`

`x\leq 12.25\text{ and} x\leq 11.75`

Upon combining our inequalities we will get,

`11.75\leq x\leq 12.25`

Therefore, the inequality
`11.75\leq x\leq 12.25` describes all the possible lengths (x), in inches, of the ribbons Jaime cut.