Question

Answer 1

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: \(x< \dfrac{2}{3}\))

\(\Rightarrow\dfrac{1}{2}x=-\dfrac{7}{8}+\dfrac{1}{3}\)

\(\Rightarrow\dfrac{1}{2}x=-\dfrac{13}{24}\)

\(\Rightarrow x=-\dfrac{13}{12}\left(tm\right)\)

Answer 2

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

Answer 3

b) x = -2

d) TH1: x = 29/12

    TH2: x = -13/12