Answer:≥2
Step-by-step explanation:
First, we need to translate the problem into algebraic expressions and equations:
[length][is][ten inches more than][twice the width]
⟹[][=][10+][2×]
⟹=10+2
==(10+2)()=22+10
[Area][is at least][28]
[][≥][28]
⟹≥28
Putting these together, we have a quadratic inequality:
22+10≥28
The most straightforward way [I know of] to solve this is to compare to zero, find the roots, and go from there:
22+10−28≥0
⟹2+5−14≥0
Finding the zeros using your favorite method — factoring, quadratic formula, etc. — yields zeros of ={−7,2} .
Since the width of the rectangle can’t be negative, our solution involves =2 . The graph of the quadratic function is concave up (due to the positive leading coefficient), meaning the function is non-negative for ≤−7 or ≥2 — giving us our solution, ≥2 !
