<s>[INST] Find number of solutions of $|2x^2-5x+3|+x-1=0$ 
Problem: Find number of solutions of $|2x^2-5x+3|+x-1=0$
Solution:
Case 1: When $2x^2-5x+3 \geq 0$
Then we get, $2x^2-5x+3+x-1=0$
x=1,1
Case 2: When $2x^2-5x+3 < 0$
Then we get, $-2x^2+5x-3+x-1=0$
x=1,2
In both cases, common value of x is 1
Hence solution is x=1

Am I doing right ??
Somebody told me solution is x=2
 [/INST] $$|2x^2-5x+3|+x-1=
\begin{cases}
2x^2-5x+3+x-1 & x\ge\frac32 \quad \text{and} \quad x\le1 \\
  -(2x^2-5x+3)+x-1 & 1\lt x\lt\frac32\\
\end{cases}\Rightarrow\begin{cases}
2x^2-4x+2 & x\ge\frac32 \quad \text{and} \quad x\le1 \\
  -2x^2+6x-4 & 1\lt x\lt\frac32\\
\end{cases}$$

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