Câu 20 trang 8 Sách bài tập (SBT) Toán 8 tập 2

Giải các phương trình sau:

\(\eqalign{
& a)\,\,\,{{x - 3} \over 5} = 6 - {{1 - 2x} \over 3} \cr
& b)\,\,{{3x - 2} \over 6} - 5 = {{3 - 2\left( {x + 7} \right)} \over 4} \cr
& c)\,\,2\left( {x + {3 \over 5}} \right) = 5 - \left( {{{13} \over 5} + x} \right) \cr
& d)\,\,{{7x} \over 8} - 5\left( {x - 9} \right) = {{20x + 1,5} \over 6} \cr} \)

Giải:

a. \(\dfrac{{x - 3}}{5} = 6 - \dfrac{{1 - 2x}}{3}\)

\(\Leftrightarrow\dfrac{{3\left( {x - 3} \right)}}{{15}} = \dfrac{{6.15}}{{15}} - \dfrac{{5\left( {1 - 2x} \right)}}{{15}}\)

 \( \Leftrightarrow 3\left( {x - 3} \right) = 6.15 - 5\left( {1 - 2x} \right)\)

\(\eqalign{  &  \Leftrightarrow 3x - 9 = 90 - 5 + 10x  \cr  &  \Leftrightarrow 3x - 10x = 90 - 5 + 9  \cr  &  \Leftrightarrow  - 7x = 94 \cr&\Leftrightarrow x =  - {{94} \over 7} \cr} \)

Vậy \(S = \left\{ { - \dfrac{{94}}{7}} \right\}\)

b.

\(\eqalign{
& {{3x - 2} \over 6} - 5 = {{3 - 2\left( {x + 7} \right)} \over 4} \cr
& \Leftrightarrow {{2\left( {3x - 2} \right)} \over {12}} - {{5.12} \over {12}} = {{3\left[ {3 - 2\left( {x + 7} \right)} \right]} \over {12}} \cr
& \Leftrightarrow 2\left( {3x - 2} \right) - 5.12 = 3\left[ {3 - 2\left( {x + 7} \right)} \right] \cr
& \Leftrightarrow 6x - 4 - 60 = 9 - 6\left( {x + 7} \right) \cr
& \Leftrightarrow 6x - 64 = 9 - 6x - 42 \cr
& \Leftrightarrow 6x + 6x = 9 - 42 + 64 \cr
& \Leftrightarrow 12x = 31 \cr
& \Leftrightarrow x = {{31} \over {12}} \cr} \)

Vậy \(S = \left\{ \dfrac{31}  {12} \right\}\)

c. 

\(\eqalign{
& 2\left( {x + {3 \over 5}} \right) = 5 - \left( {{{13} \over 5} + x} \right) \cr
& \Leftrightarrow 2x + {6 \over 5} = {{25} \over 5} - {{13} \over 5} - x \cr
& \Leftrightarrow 2x + {6 \over 5} = {{12} \over 5} - x \cr
& \Leftrightarrow 2x + x = {{12} \over 5} - {6 \over 5} \cr
& \Leftrightarrow 3x = {6 \over 5} \cr
& \Leftrightarrow x = {6 \over 5}:3 \cr
& \Leftrightarrow x = {2 \over 5} \cr} \)

Vậy \(S = \left\{ {\dfrac{2 }{ 5}} \right\}\)

d. 

\(\eqalign{
& {{7x} \over 8} - 5\left( {x - 9} \right) = {{20x + 1,5} \over 6} \cr
& \Leftrightarrow {{3.7x} \over {24}} - {{24.5\left( {x - 9} \right)} \over {24}} = {{4.\left( {20x + 1,5} \right)} \over {24}} \cr
& \Leftrightarrow 3.7x - 24.5\left( {x - 9} \right) = 4\left( {20x + 1,5} \right) \cr
& \Leftrightarrow 21x - 120\left( {x - 9} \right) = 80x + 6 \cr
& \Leftrightarrow 21x - 120x + 1080 = 80x + 6 \cr
& \Leftrightarrow 21x - 120x - 80x = 6 - 1080 \cr
& \Leftrightarrow - 179x = - 1074 \cr
& \Leftrightarrow x = \left( { - 1074} \right):\left( { - 179} \right) \cr
& \Leftrightarrow x = 6 \cr} \)

Phương trình có nghiệm \(x = 6\)

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