Property 5
- The type of the variable is important particularly when determining the minimum or maximum value of the variable.
- If the variable is an integer \((\mathbb{Z})\); the equation is solved by giving a value to the variable according to the inequality.
- If the variable is an real number \((\mathbb{R})\); the equation is solved by performing the interval solutions.
1.
\(x\in\mathbb{R}\)
\(3<x\le8\)
\(\Rightarrow ?<x^2<?\)
2.
\(x\in\mathbb{R}\)
\(-4<x\le-1\)
\(\Rightarrow ?<x^2<?\)
3.
\(x\in\mathbb{R}\)
\(-2<x<4\)
\(\Rightarrow ?<x^2<?\)
4.
\(x,y\in\mathbb{R}\)
\(-3<x<4\)
\(-4<y\le2\)
\(\Rightarrow ?<x\cdot y<?\)
5.
\(x,y\in\mathbb{R}\)
\(-5\le x<3\)
\(-6\le y<2\)
\(\Rightarrow ?<x\cdot y<?\)
6.
\(x,y\in\mathbb{R}\qquad(x+y)\in\mathbb{Z}\)
\(-3<x<4\)
\(-2<y<6\)
\(\Rightarrow\max(x+y)=?\)
7.
\(x,y\in\mathbb{Z}\)
\(-3<x<4\)
\(-2\le y<6\)
\(\Rightarrow\max(x+y)=?\)
8.
\(x,y\in\mathbb{Z}\)
\(-6<x<3\)
\(-8<y\le8\)
\(\Rightarrow\max(x-y)=?\)
9.
\(x,y\in\mathbb{R}\)
\((x+y)\in\mathbb{Z}\)
\(-5<x\le4\)
\(-3\le y<5\)
\(\Rightarrow\min(x+y)=?\)
10.
\(x,y\in\mathbb{R}\)
\((x-y)\in\mathbb{Z}\)
\(-6<x<4\)
\(-3<y<5\)
\(\Rightarrow\max(x-y)=?\)
11.
\(x,y\in\mathbb{Z}\)
\(-3<x<5\)
\(-2<y<4\)
\(\Rightarrow\max(2x+y)=?\)
12.
\(x,y\in\mathbb{Z}\)
\(-2\le x<4\)
\(-4\le y<3\)
\(\Rightarrow\max(3x-y)=?\)
13.
\(x,y\in\mathbb{R}\)
\((x-2y)\in\mathbb{Z}\)
\(-4<x\le5\)
\(-9\le y\le4\)
\(\Rightarrow\min(x-2y)=?\)