2 POINTS
which of the following is the solution to | x-13|<18

 -5 < x < 31

Step-by-step explanation:

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequality entered

     |x-13| < 18  

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x-13|

For the Negative case we'll use -(x-13)  

For the Positive case we'll use (x-13)  

Step  3  :

Solve the Negative Case

     -(x-13) < 18  

    Multiply

     -x+13 < 18  

    Rearrange and Add up

     -x < 5  

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     x > -5  

    Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

     (x-13) < 18  

    Rearrange and Add up

     x < 31  

    Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

   -5 < x < 31

answer: howdy

step-by-step explanation:

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: