Write an absolute value inequality that represents the situation. then solve the inequality. the difference between the perimeters of the figures is less than or equal to 3.

All real numbers greater than or equal to 2.5 and less than or equal to 5.5

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the perimeter of the square

The perimeter of the square is

where

b is the length side of the square

substitute the given value

step 2

Find the perimeter of rectangle

The perimeter of rectangle is

where

L is the length of rectangle

W is the width of rectangle

substitute the given values

step 3

we know that

The difference between the perimeters of the figures is less than or equal to 3

Write an absolute value inequality that represents the situation

Solve the absolute value

First case (positive value)

The solution is the interval -----> (-∞,5.5]

Second case (negative value)

Multiply by -1 both sides

The solution is the interval -----> [2.5,∞)

The solution of the absolute value for x is

[2.5,∞) ∩ (-∞,5.5] =[2.5,5.5]

All real numbers greater than or equal to 2.5 and less than or equal to 5.5