Case 1 :\(x< -\dfrac{1}{2}\Leftrightarrow\left\{{}\begin{matrix}2x-3< -4< 0\\2x+1< 0\end{matrix}\right.\)

\(\Rightarrow3-2x-2x-1=4\Rightarrow4x=-2\Rightarrow x=-\dfrac{1}{2}\)(asburd)

Case 2 :\(-\dfrac{1}{2}\le x< \dfrac{3}{2}\Rightarrow\left\{{}\begin{matrix}2x-3< 0\\2x+1\ge0\end{matrix}\right.\)

\(\Rightarrow3-2x+2x+1=4\Rightarrow4=4\) (true)

Case 3 :\(x\ge\dfrac{3}{2}\Rightarrow\left\{{}\begin{matrix}2x-3\ge0\\2x+1\ge4>0\end{matrix}\right.\)

\(\Rightarrow2x-3+2x+1=4\Rightarrow4x-2=4\Rightarrow4x=6\Rightarrow x=\dfrac{3}{2}\)(true)

So\(-\dfrac{1}{2}\le x\le\dfrac{3}{2}\)

Case 1 :x<−12⇔{2x−3<−4<02x+1<0

⇒3−2x−2x−1=4⇒4x=−2⇒x=−12

(asburd)

Case 2 :−12≤x<32⇒{2x−3<02x+1≥0

⇒3−2x+2x+1=4⇒4=4

 (true)

Case 3 :x≥32⇒{2x−3≥02x+1≥4>0

⇒2x−3+2x+1=4⇒4x−2=4⇒4x=6⇒x=32

(true)

So−12≤x≤32