=> |x - \(\frac{3}{2}\)| + |2x - 3| = 7,5

=> |2x - 3| + 2.|2x - 3| = 2.7,5

=> 3.|2x - 3| = 15

=> |2x - 3| = 5 => 2x - 3 = 5 hoặc 2x - 3 = -5

+) 2x - 3 = 5 => 2x = 8 => x = 4

+) 2x - 3 = - 5 => x = -1

Vậy x \(\in\) {-1; 4}

|x-1,5| + 2|x-1,5| =7,5

3|x-1,5| =7,5

|x-1,5| = 2,5

+ x -1,5 = 2,5 => x =4

+ x-1,5 = -2,5 => x =-1

\(\left|x-1,5\right|=7,5-\left|2x-3\right|\)

=> \(\orbr{\begin{cases}x-1,5=7,5-\left(2x-3\right)\\x-1,5=7,5-\left[-\left(2x-3\right)\right]\end{cases}}\)=> \(\orbr{\begin{cases}x-1,5=7,5-2x+3\\x-1,5=7,5+2x-3\end{cases}}\)

=> \(\orbr{\begin{cases}x-1,5=10,5-2x\\x-1,5=4,5+2x\end{cases}}\)=> \(\orbr{\begin{cases}x+2x=10,5+1,5\\x-2x=4,5+1,5\end{cases}}\)=. \(\orbr{\begin{cases}3x=12\\-x=6\end{cases}}\)=> \(\orbr{\begin{cases}x=4\\x=-6\end{cases}}\)

\(\left|x-1\right|+2C=\left|x-1,5\right|+\left|1-x\right|\\ \Leftrightarrow\left|x-1\right|+2C=\left|x-1,5\right|+\left|x-1\right|\\ \Rightarrow2C=\left|x-1,5\right|\ge0\\ \Rightarrow C\ge0\)

Để C=0 thì

\(\left|x-1,5\right|=0\\ \Leftrightarrow x-1,5=0\\ \Leftrightarrow x=1,5\)

Vậy...