Let `{x}` and `[x]` denotes the fraction fractional and integral part of a real number `(x)`, respectively. Solve `|2x-1+=3[x]+2[x]`.

Explanation

To solve the equation \( |2x - 1| = 3[x] + 2\{x\} \), where \([x]\) is the integral part of \(x\) and \(\{x\}\) is the fractional part of \(x\), we will break it down into two cases based on the definition of the absolute value.

### Step 1: Define the Cases
The absolute value function \( |2x - 1| \) leads us to two cases:
1. Case 1: \( 2x - 1 \geq 0 \) (i.e., \( x \geq \frac{1}{2} \))
2. Case 2: \( 2x - 1 < 0 \) (i.e., \( x < \frac{1}{2} \))

### Step 2: Solve Case 1
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