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Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 18 feet. The perimeter of the dog run must be at least 42 feet and no more than 72 feet. Use a compound inequality to find the range of values for the width of the dog run

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JeanaShupp

Answer: [tex]3\leq x \leq 18[/tex]

Step-by-step explanation:

Given, the length of the rectangular dog run is 18 feet.

Formula: Perimeter = 2 ( length + width)

Let width be x.

Then, Perimeter = 2 (18 + x ) feet

The perimeter of the dog run must be at least 42 feet and no more than 72 feet.

That is  

[tex]42\leq 2 (x+18)\leq 72[/tex]

Divide inequality by 2, we get

[tex]21\leq 18+x\leq 36[/tex]

Subtract 18 from each side, we get

[tex]3\leq x \leq 18[/tex]

Required inequality : [tex]3\leq x \leq 18[/tex]

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