b) \(\dfrac{1}{2}x+\dfrac{2}{3}x-1=-3\dfrac{1}{3}\)
\(\Rightarrow x\cdot\left(\dfrac{1}{2}+\dfrac{2}{3}\right)-1=-\dfrac{10}{3}\)
\(\Rightarrow\dfrac{7}{6}x-1=-\dfrac{10}{3}\)
\(\Rightarrow\dfrac{7}{6}x=-\dfrac{10}{3}+1\)
\(\Rightarrow\dfrac{7}{6}x=-\dfrac{7}{3}\)
\(\Rightarrow x=-\dfrac{7}{3}:\dfrac{7}{6}\)
\(\Rightarrow x=-2\)
d) \(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|-\dfrac{3}{2}=\dfrac{1}{4}\)
\(\Rightarrow2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{1}{4}+\dfrac{3}{2}\)
\(\Rightarrow2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{7}{4}\)
\(\Rightarrow\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{7}{8}\)
TH1: \(\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{8}\) (ĐK: \(x\ge\dfrac{2}{3}\))
\(\Rightarrow\dfrac{1}{2}x=\dfrac{7}{8}+\dfrac{1}{3}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{29}{24}\)
\(\Rightarrow x=\dfrac{29}{12}\left(tm\right)\)
TH2: \(\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{7}{8}\) (ĐK: \(x< \dfrac{2}{3}\))
\(\Rightarrow\dfrac{1}{2}x=-\dfrac{7}{8}+\dfrac{1}{3}\)
\(\Rightarrow\dfrac{1}{2}x=-\dfrac{13}{24}\)
\(\Rightarrow x=-\dfrac{13}{12}\left(tm\right)\)
b) 1/2 x + 2/3 x - 1 = -3 1/3
7/6 x - 1 = -10/3
7/6 x = -10/3 + 1
7/6 x = -7/3
x = -7/3 : 7/6
x = -2
d) 2|1/2 x - 1/3| - 3/2 = 1/4
2|1/2 x - 1/3| = 1/4 + 3/2
2|1/2 x - 1/3| = 7/4
|1/2 x - 1/3| = 7/4 : 2
|1/2 x - 1/3| = 7/8
1/2 x - 1/3 = 7/8 và 1/2 x - 1/3 = -7/8
*) 1/2 x - 1/3 = 7/8
1/2 x = 7/8 + 1/3
1/2 x = 29/24
x = 29/24 : 1/2
x = 29/12
*) 1/2 x - 1/3 = -7/8
1/2 x = -7/8 + 1/3
1/2 x = -13/24
x = -13/24 : 1/2
x = -13/12
b) x = -2
d) TH1: x = 29/12
TH2: x = -13/12
