Property 3
In rational expressions the expressions with equal denominators are gathered on one side of the equation.
The values that make the denominator zero are removed from the solution set.
1.
\(\samefrac{x}{x-1}+x+2<\samefrac{1}{x-1}\)
\(\Rightarrow\text{S.S.}=?\)
2.
\(\samefrac{x}{x+2}+3<x-\samefrac{2}{x+2}\)
\(\Rightarrow\text{S.S.}=?\)
3.
\(\samefrac{x}{x-2}+2(x-1)<\samefrac{2}{x-2}\)
\(\Rightarrow\text{S.S.}=?\)
4.
\(\samefrac{3}{x-3}+x>\samefrac{x}{x-3}-8\)
\(\Rightarrow\text{S.S.}=?\)
5.
\(\samefrac{2x}{2x+3}+\samefrac{1}{x-1}-2<\samefrac{x}{x-1}-\samefrac{3}{2x+3}\)
\(\Rightarrow\text{S.S.}=?\)
Property 4
The intersection of the solution sets is taken into consideration.
1.
\(-1\le\samefrac{x-3}{2}<3\)
\(\Rightarrow\text{S.S.}=?\)
2.
\(x-3<2x+1<x+8\)
\(\Rightarrow\text{S.S.}=?\)
3.
\(x-4<3x+2\le x+6\)
\(\Rightarrow\text{S.S.}=?\)
4.
\(2x-4<6\)
\(x+3>1\)
\(\Rightarrow\text{S.S.}=?\)
5.
\(10>3x+1\)
\(x-8<2x+1\)
\(\Rightarrow\text{S.S.}=?\)
6.
\(3x-2>4\)
\(x-1<1\)
\(\Rightarrow\text{S.S.}=?\)
7.
\(3(x-2)\le2(x+1)\)
\(x-3>1\)
\(\Rightarrow\text{S.S.}=?\)