(1) Find algebraically the solution set of the inequality: $$ |2 x-3|+37 $$

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(1) Find algebraically the solution set of the inequality: $$ |2 x-3|+3>7 $$

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Solve the equation $$ |2x-3|+3>7 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$\left|2x-3 ight|+3>7$$ - step1: Rearrange the terms: $$\left|2x-3 ight|>4$$ - step2: Separate into possible cases: $$\begin{align}&2x-3>4\&2x-3<-4\end{align}$$ - step3: Solve the inequality: $$\begin{align}&x>\frac{7}{2}\&x<-\frac{1}{2}\end{align}$$ - step4: Find the union: $$x \in \left(-\infty,-\frac{1}{2} ight)\cup \left(\frac{7}{2},+\infty ight)$$ The solution set of the inequality $$ |2x-3|+3>7 $$ is $$ x \in (-\infty,-\frac{1}{2})\cup (\frac{7}{2},+\infty) $$. $$ x \in (-\infty,-\frac{1}{2})\cup (\frac{7}{2},+\infty) $$

(1) Find algebraically the solution set of the inequality:

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