I 2x-3 I = I x+1 I
2x-3 = x+1
x+1 - 2x+3=0
x (1-2) +1+3=0
-1x +4 =0
-1x = 0-4
-1x =-4
x = -4 : -1
x =4
Trả lời:
\(\left|2x-3\right|=\left|x+1\right|\)
\(\Rightarrow2x-3=x+1\) hoặc \(2x-3=-\left(x+1\right)\)
TH1: \(2x-3=x+1\)
\(2x-x=1+3\)
\(x=4\)
TH2: \(2x-3=-\left(x+1\right)\)
\(2x-3=-x-1\)
\(2x+x=-1+3\)
\(3x=2\)
\(x=\frac{2}{3}\)
Vậy \(x=4;x=\frac{2}{3}\)
\(\left|\frac{1}{3}-x\right|-\left|-\frac{2}{3}\right|=\left|\frac{3}{4}\right|\)
\(\Leftrightarrow\frac{1}{3}-x-\frac{2}{3}=\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{3}-x=\frac{3}{4}+\frac{2}{3}\)
\(\Leftrightarrow\frac{1}{3}-x=\frac{17}{12}\)
\(\Leftrightarrow x=\frac{1}{3}-\frac{17}{12}=\frac{4}{12}-\frac{17}{12}=\frac{-13}{12}\)
\(\left|\frac{1}{3}-x\right|-\left|-\frac{2}{3}\right|=\left|\frac{3}{4}\right|\)
\(\left|\frac{1}{3}-x\right|-\frac{2}{3}=\frac{3}{4}\)
\(\left|\frac{1}{3}-x\right|=\frac{3}{4}+\frac{2}{3}\)
\(\left|\frac{1}{3}-x\right|=\frac{17}{12}\)
\(\Rightarrow\orbr{\begin{cases}\frac{1}{3}-x=\frac{17}{12}\\\frac{1}{3}-x=\frac{-17}{12}\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=\frac{-13}{12}\\x=\frac{21}{12}\end{cases}}\)
Vậy \(x=\frac{-13}{12};x=\frac{21}{12}\)
