a rectangular pen for a pet is 7 feet longer than it is wide. GIive possible values for the width W of the pen if its area must be between 228 and 100 square feet, inclusively.

The width of the pen ranges from the smaller value of the width, ???, feet to the larger value of the width???, feet, inclusively.

Question

a rectangular pen for a pet is 7 feet longer than it is wide. GIive  possible values for the width W of the pen if its area must be between 228 and 100 square feet, inclusively.

The width of the pen ranges from the smaller value of the width,  ???, feet to the larger value of the width???, feet, inclusively.

anonymous · Answer

so you know that if the length is x the width is x+7

anonymous · Answer

and you also know that the area is 
$$x(x+7)$$ and that 
$$100\leq x(x+7)\leq 228$$

anonymous · Answer

can you solve this?

anonymous · Answer

you have to solve them separately. first solve 
$$100\leq x^2+7x$$ via 
$$0\leq x^2+7x-100$$
then solve the resulting quadratic

anonymous · Answer

likewise for 
$$x^2+7x\leq228$$ solve 
$$x^2+7x-228 \leq 0$$