if x belongs to INTEGER find the smallest value of x which satisfies the inequation
2x+5/2>5x/3+2 

Dear Student,

Please find below the solution to the asked query:

We have equation : $2 x +\frac{5}{2} > \frac{5 x}{3} + 2$ , First we siplify that , As :

$$\begin{gathered} \Rightarrow 2 x -\frac{5 x}{3} >2 -\frac{5}{2} \\ \Rightarrow \frac{6 x -5 x}{3} >\frac{4 -5}{2} \\ \Rightarrow \frac{x}{3} >\frac{- 1}{2} \\ \Rightarrow x >\frac{- 3}{2} \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{>}\mathbf{-}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{5} \end{gathered}$$
Therefore,

Smallest value of x which satisfies the inequation = - 1                                          ( Ans )

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