\(\left|0,75-\frac{5}{4}x\right|=\left|-\frac{2}{3}x+\frac{5}{6}\right|\)
\(\Rightarrow\left|0,75-\frac{5}{4}x\right|-\left|-\frac{2}{3}x+\frac{5}{6}\right|=0\)
Mà GTTĐ luôn lớn hơn hoặc bằng 0
=> +) \(0,75-\frac{5}{4}x=0\)
\(\frac{5}{4}x=0,75\)
\(x=\frac{3}{5}\)
+) \(-\frac{2}{3}x+\frac{5}{6}=0\)
\(-\frac{2}{3}x=-\frac{5}{6}\)
\(x=\frac{5}{4}\)
Vậy,.........
\(|\)0,75 - 5/4x\(|\)= \(|\)-2/3x +5/6 \(|\)
\(\Leftrightarrow\)0,75-5/4x = -2/3x+5/6 hoặc 0,75-5/4x=-(-2/3x+5/6)
TH1: 0,75-5/4x = -2/3x+5/6
\(\Leftrightarrow\)-5/4x+2/3x= 5/6-0,75
\(\Leftrightarrow\)-7/12x= 1/12
\(\Leftrightarrow\)x = 1/12 \(\div\)(-7/12)
\(\Leftrightarrow\)x = -1/7
TH2: 0,75-5/4x=-(-2/3x+5/6)
\(\Leftrightarrow\)0,75 - 5/4x= 2/3x-5/6
\(\Leftrightarrow\)-5/4x-2/3x = -5/6-0.75
\(\Leftrightarrow\)-23/12x= -19/12
\(\Leftrightarrow\)x=-(19/12)\(\div\)(-23/12)
\(\Leftrightarrow\)x=19/23
Vậy, x =-1/7 hoặc x= 19/23
từ đề bài ta có thể suy ra
0,75-5/4 x= -2/3x + 5/6
-5/4x+2/3x = -0,75 + 5/6
-7/12x = 19/12
x=-19/7
\(|0.75-\frac{5}{4}x|=|-\frac{2}{3}x+\frac{5}{6}|\)
\(\Rightarrow\orbr{\begin{cases}0.75-\frac{5}{4}x=-\frac{2}{3}x+\frac{5}{6}\\-0.75+\frac{5}{4}x=-\frac{2}{3}x+\frac{5}{6}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{3}{4}-\frac{5}{6}=-\frac{2}{3}x+\frac{5}{4}x\\\frac{5}{4}x--\frac{2}{3}x=\frac{5}{6}+\frac{3}{4}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}-\frac{1}{12}=x\cdot\left(-\frac{2}{3}+\frac{5}{4}\right)\\x\cdot\left(\frac{5}{4}+\frac{2}{3}\right)=\frac{19}{12}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x\cdot\frac{7}{12}=-\frac{1}{12}\\x\cdot\frac{23}{12}=\frac{19}{12}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{7}\\x=\frac{19}{23}\end{cases}}\)
