\(\left|\frac{5}{4}-\frac{x}{2}\right|=x-1\)
\(\Leftrightarrow\frac{\left|5-2x\right|}{4}=x-1\)
\(\Leftrightarrow\left|5-2x\right|=4x-4\)
+ ) \(x< \frac{5}{2}\)
pt \(\Leftrightarrow5-2x=4x-4\)
\(\Leftrightarrow-2x-4x=-4-5\)
\(\Leftrightarrow-6x=-9\)
\(\Leftrightarrow x=\frac{3}{2}\) ( nhận )
+ ) \(x\ge\frac{5}{2}\)
pt \(2x-5=4x-4\)
\(\Leftrightarrow2x-4x=-4+5\)
\(\Leftrightarrow-2x=1\)
\(\Leftrightarrow x=-\frac{1}{2}\) ( loại )
Vậy ..............
\(\left|\frac{5}{4}-\frac{x}{2}\right|=x-1\)
\(\Rightarrow\left[\begin{array}{nghiempt}\frac{5}{4}-\frac{x}{2}=x-1\\\frac{x}{2}-\frac{5}{4}=x-1\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}\frac{9}{4}=\frac{3x}{2}\\-\frac{x}{2}=\frac{1}{4}\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{3}{2}\\x=-\frac{1}{2}\end{array}\right.\)
