Answer:
(1). The solution of inequality is 15>w. It means the width of the rectangle is less than 15 inches.
(2) The solution set is w={10,11,12,13,14}.
Step-by-step explanation:
The given inequality is
[tex]80-2w>50[/tex]
where, w is the width of the rectangle in inches.
Add 2w on both sides.
[tex]80-2w+2w>50+2w[/tex]
[tex]80>50+2w[/tex]
Subtract 50 from both sides.
[tex]80-50>50+2w-50[/tex]
[tex]30>2w[/tex]
Divide both sides by 2.
[tex]\frac{30}{2}>w[/tex]
[tex]15>w[/tex] ... (1)
The solution of inequality is 15>w. It means the width of the rectangle is less than 15 inches.
The width must be at least 10 inches and a whole number.
[tex]10\leq w[/tex] .... (2)
Using (1) and (2), we get
[tex]10\leq w<15[/tex]
[tex]w=\{10,11,12,13,14\}[/tex]
Therefore the solution set is w={10,11,12,13,14}.
