Question

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Answer 1

$a) 2.(\dfrac{1}{2}x-\dfrac{1}{3})-\dfrac{3}{2}=\dfrac{1}{4}$

$2.(\dfrac{1}{2}x-\dfrac{1}{3})= \dfrac{1}{4}+\dfrac{3}{2}$

$2.(\dfrac{1}{2}x-\dfrac{1}{3})= \dfrac{7}{4}$

$\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{4}:2$

$\dfrac{1}{2}x-\dfrac{1}{3}= \dfrac{7}{8}$

$\dfrac{1}{2}x= \dfrac{7}{8}+\dfrac{1}{3}$

$\dfrac{1}{2}x=\dfrac{21}{24}+\dfrac{8}{24}$

$\dfrac{1}{2}x= \dfrac{29}{24}$

$x= \dfrac{29}{24}:\dfrac{1}{2}$

$x= \dfrac{29}{24}.2$

$x= \dfrac{29}{12}$

$\text{Vậy x=$\dfrac{29}{12}$}$

$b) (\dfrac{1}{2}+2x).(2x-3)=0$

$\text{XÉT 2TH:}$

$+) TH1: \dfrac{1}{2}+2x=0$

$2x= -\dfrac{1}{2}$

$x= \dfrac{-1}{2}.\dfrac{1}{2}$

$x= \dfrac{-1}{4}$

$+) TH2: 2x-3=0$

$2x=3$

$x= \dfrac{3}{2}$

$\text{Vậy x ∈ {$\dfrac{-1}{4};\dfrac{3}{2}$}}$

$c) (4x-5).(\dfrac{5}{4}x-2)=0$

$\text{+) XÉT 2TH:}$

$+) TH1: 4x-5=0$

$4x=5$

$x=\dfrac{5}{4}$

$+) TH2: \dfrac{5}{4}x-2=0$

$\dfrac{5}{4}x=2$

$x= 2:\dfrac{5}{4}$

$x= \dfrac{8}{5}$

$\text{Vậy x ∈ {$\dfrac{5}{4}:\dfrac{8}{5}$}}$

$d) \dfrac{1}{4}-(2x+\dfrac{1}{2})^2=0$

$(2x+\dfrac{1}{2})^2=\dfrac{1}{4}$

$(2x+\dfrac{1}{2})^2= (±\dfrac{1}{2})^2$

$\text{+) XÉT 2TH:}$

$+) TH1: 2x+\dfrac{1}{2}=\dfrac{1}{2}$

$2x= \dfrac{1}{2}-\dfrac{1}{2}$

$2x=0$

$x=0$

$+) TH2: 2x+\dfrac{1}{2}=-\dfrac{1}{2}$

$2x= \dfrac{-1}{2}-\dfrac{1}{2}$

$2x=-1$

$x= -\dfrac{1}{2}$

$\text{Vậy x ∈ {0;$-\dfrac{1}{2}$}}$

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Answer 2

$a) 2.(\dfrac{1}{2}x-\dfrac{1}{3})-\dfrac{3}{2}=\dfrac{1}{4}$

$2.(\dfrac{1}{2}x-\dfrac{1}{3})= \dfrac{1}{4}+\dfrac{3}{2}$

$2.(\dfrac{1}{2}x-\dfrac{1}{3})= \dfrac{7}{4}$

$\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{4}:2$

$\dfrac{1}{2}x-\dfrac{1}{3}= \dfrac{7}{8}$

$\dfrac{1}{2}x= \dfrac{7}{8}+\dfrac{1}{3}$

$\dfrac{1}{2}x=\dfrac{21}{24}+\dfrac{8}{24}$

$\dfrac{1}{2}x= \dfrac{29}{24}$

$x= \dfrac{29}{24}:\dfrac{1}{2}$

$x= \dfrac{29}{24}.2$

$x= \dfrac{29}{12}$

$\text{Vậy x=$\dfrac{29}{12}$}$

$b) (\dfrac{1}{2}+2x).(2x-3)=0$

$\text{XÉT 2TH:}$

$+) TH1: \dfrac{1}{2}+2x=0$

$2x= -\dfrac{1}{2}$

$x= \dfrac{-1}{2}.\dfrac{1}{2}$

$x= \dfrac{-1}{4}$

$+) TH2: 2x-3=0$

$2x=3$

$x= \dfrac{3}{2}$

$\text{Vậy x ∈ {$\dfrac{-1}{4};\dfrac{3}{2}$}}$

$c) (4x-5).(\dfrac{5}{4}x-2)=0$

$\text{+) XÉT 2TH:}$

$+) TH1: 4x-5=0$

$4x=5$

$x=\dfrac{5}{4}$

$+) TH2: \dfrac{5}{4}x-2=0$

$\dfrac{5}{4}x=2$

$x= 2:\dfrac{5}{4}$

$x= \dfrac{8}{5}$

$\text{Vậy x ∈ {$\dfrac{5}{4}:\dfrac{8}{5}$}}$

$d) \dfrac{1}{4}-(2x+\dfrac{1}{2})^2=0$

$(2x+\dfrac{1}{2})^2=\dfrac{1}{4}$

$(2x+\dfrac{1}{2})^2= (±\dfrac{1}{2})^2$

$\text{+) XÉT 2TH:}$

$+) TH1: 2x+\dfrac{1}{2}=\dfrac{1}{2}$

$2x= \dfrac{1}{2}-\dfrac{1}{2}$

$2x=0$

$x=0$

$+) TH2: 2x+\dfrac{1}{2}=-\dfrac{1}{2}$

$2x= \dfrac{-1}{2}-\dfrac{1}{2}$

$2x=-1$

$x= -\dfrac{1}{2}$

$\text{Vậy x ∈ {0;$-\dfrac{1}{2}$}}$

Số thứ tự	Loại hàng	Số lượng (quyển)	Giá đơn vị (đồng)	Tổng số tiền (đồng)
1	Vở loại 1	35	2000	...
2	Vở loại 2	42	1500	...
3	Vở loại 3	38	1200	...
Cộng:				...

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