Solve `x+1|+|2x-3|=4.`

Explanation

To solve the equation \( |x + 1| + |2x - 3| = 4 \), we need to consider the different cases based on the expressions inside the absolute values. The critical points where the expressions change sign are at \( x = -1 \) and \( x = \frac{3}{2} \). We will analyze the problem in three intervals:

1. \( x < -1 \)
2. \( -1 \leq x < \frac{3}{2} \)
3. \( x \geq \frac{3}{2} \)

### Case 1: \( x < -1 \)

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