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explain to me a clear, detailed explanation of all necessary processes about Inequalities with variables on both sides

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Let us consider an inequality with variable in the both sides of the inequality.


2x-5\leq3-2x

Now, first, we will take all the terms with variable in one side of the inequality and the constant terms in the other side.

It follows


2x+2x\leq3+5

Now, we will solve the inequality for x.


\begin{gathered} 4x\leq8 \\ x\leq2 \end{gathered}

Hence, the solution of the considered inequation is


x\leq2

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