Property 2
In inequalities all of the expressions should be in multiplication or division position. Likewise all expressions should be placed in one side of the inequality on the other side there should be only 0.
In given inequality it can be written in the form of a multiplication of linear equation, the roots of the equation are placed on the number line. Sign of only one region is found. Sign of the other regions rely on the symbols of roots.
Example
\(\samefrac{(2-x)(x+5)}{x-3}\ge0\)
Answer
\(2-x=0\Rightarrow x=2\)
\(x+5=0\Rightarrow x=-5\)
\(x-3=0\Rightarrow x=3\)
| x | −∞ | −5 | 2 | 3 | +∞ | ||
|---|---|---|---|---|---|---|---|
| f(x) | + | ○ | − | ○ | + | ○ | − |
\(S.S.=(-\infty,-5]\cup[2,3)\)
1.
\(\samefrac{x-2}{x+1}<0\)
\(\Rightarrow S.S.=?\)
2.
\(\samefrac{x+1}{3-x}\ge0\)
\(\Rightarrow S.S.=?\)
3.
\((1-x)(x+3)>0\)
\(\Rightarrow S.S.=?\)
4.
\(\samefrac{(x-1)(x-3)}{x+4}>0\)
\(\Rightarrow S.S.=?\)
5.
\(\samefrac{x^2+x-12}{x-2}\le0\)
\(\Rightarrow S.S.=?\)
6.
\(\samefrac{(x+2)(x-3)}{x-4}\ge0\)
\(\Rightarrow S.S.=?\)
7.
\(\samefrac{(7-x)(x+5)}{(x-1)(x-10)}\ge0\)
\(\Rightarrow S.S.=?\)
8.
\(\samefrac{x^2-4}{x^2+5x+6}\le0\)
\(\Rightarrow S.S.=?\)