Given:
[tex]\frac{3}{4}(x-2)\text{ }<\text{ x -2}[/tex]
Opening the bracket:
[tex]\frac{3x}{4}\text{ - }\frac{6}{4}\text{ }<\text{ x - 2}[/tex]
Collect like terms:
[tex]\begin{gathered} \frac{3x}{4}-x\text{ }<\text{ }\frac{6}{4}\text{ - 2} \\ \frac{3x-4x}{4}\text{ }<\text{ }\frac{6-8}{4} \\ -\frac{x}{4}\text{ }<\text{ }\frac{-2}{4} \end{gathered}[/tex]
Solving for x:
[tex]\begin{gathered} -\frac{x}{4}\text{ }<\text{ }\frac{-2}{4} \\ -x\text{ }<\text{ -2} \\ x\text{ > 2} \end{gathered}[/tex]
The solution in interval notation:
[tex](2\text{ , }\infty\text{ )}[/tex]
The solution on a graph:
The solution on a number line:
