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

Step-by-step explanation:

You are given the rectangle with sides of (x + 1) units and 3 units and the square with the side of x units.

The perimeter of the rectangle is

The perimeter of the square is

We do not know whose perimeter is 3 units greater (or equal to), so the absolute value of the difference of these perimeters should be less than or equal to 3.

Hence,

Solve this inequality:

The formula for calculating the perimeter of a square is expressed as:

P = 4L

L is the side length of the square

For the square with side length "x"

The area of the rectangle is expressed as 2(L+W)

L is the length

W is the width

For the given rectangle with length 3 and width (x+1)

The difference between the perimeters of the figure will be expressed as:

If the modulus value is positive:

If the modulus value is negative:

Combining both inequalities, the required solution will be

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step-by-step explanation: