Question

the rectangular pen for a pet is 6 feet longer athan it is wide. Give possible values for the width W of the pen if its area must be between 187 and 520 square feet, inclusively.

Answer 1

is a start
\[187\leq W(W+6)\leq520\]

Answer 2

do you know how to go from here? you are going to have to solve two inequalities
\[w(w+6)\leq 520\]
\[w^2+6w\leq 520\]
\[w^2+6w-520\leq 0\]
\[(w-20)(w+26)\leq 0\] so
\[-26\leq w \leq 20\]

Answer 3

then you have to solve
\[187\leq w^2+6w\]
\[0\leq w^2+6w-187\]
\[0\leq(w-11)(w+17)\]
so either
\[w\leq -17\] or
\[w\geq 11\]

Answer 4

a pain but at least both of these factored. now put the inequalities together to get
\[11\leq w\leq 20\]

Answer 5

thank u.......