Question

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

b)\(\frac{3x-2}{6}-5=\frac{3-2\left(x+7\right)}{4}\)

c)\(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)

d)\(\frac{7x}{8}-5\left(x-9\right)=\frac{\left(20x+1.5\right)}{6}\)

Answer 1

\( a)\dfrac{{x - 3}}{5} = 6 - \dfrac{{1 - 2x}}{2}\\ \Leftrightarrow 2\left( {x - 3} \right) = 60 - 5\left( {1 - 2x} \right)\\ \Leftrightarrow 2x - 6 = 60 - 5 + 10x\\ \Leftrightarrow 8x = - 61\\ \Leftrightarrow x = - \dfrac{{61}}{8}\\ b)\dfrac{{3x - 2}}{6} - 5 = \dfrac{{3 - 2\left( {x + 7} \right)}}{4}\\ \Leftrightarrow 2\left( {3x - 2} \right) - 60 = 3\left( { - 11 - 2x} \right)\\ \Leftrightarrow 6x - 4 - 60 = - 33 - 6x\\ \Leftrightarrow 12x = 31\\ \Leftrightarrow x = \dfrac{{31}}{{12}} \)

Answer 2

\(a.\frac{x-3}{5}=6-\frac{1-2x}{2}\\\Leftrightarrow \frac{2\left(x-3\right)}{10}=\frac{60}{10}-\frac{5\left(1-2x\right)}{10}\\ \Leftrightarrow2\left(x-3\right)=60-5\left(1-2x\right)\\\Leftrightarrow 2x-6=60-5+10x\\\Leftrightarrow 2x-10x=6+60-5\\\Leftrightarrow -8x=61\\ \Leftrightarrow x=-\frac{61}{8}\)

Vậy nghiệm của phương trình trên là \(-\frac{61}{8}\)

Answer 3

https://i.imgur.com/BgP6oOl.jpg

Answer 4

\( c)2\left( {x + \dfrac{3}{5}} \right) = 5 - \left( {\dfrac{{13}}{5} + x} \right)\\ \Leftrightarrow 2x + \dfrac{6}{5} = \dfrac{{12}}{5} - x\\ \Leftrightarrow 3x = \dfrac{6}{5}\\ \Leftrightarrow x = \dfrac{2}{5}\\ d)\dfrac{{7x}}{8} - 5\left( {x - 9} \right) = \dfrac{{20x + 1,5}}{6}\\ \Leftrightarrow 21x - 120x + 1080 = 2\left( {40x + 3} \right)\\ \Leftrightarrow - 179x = - 1074\\ \Leftrightarrow x = 6 \)

Answer 5

\(b.\frac{3x-2}{6}-5=\frac{3-2\left(x+7\right)}{4}\\\Leftrightarrow \frac{2\left(3x-2\right)}{12}-\frac{60}{12}=\frac{3\left[3-2\left(x+7\right)\right]}{12}\\ \Leftrightarrow2\left(3x-2\right)-60=3\left[3-2\left(x+7\right)\right]\\\Leftrightarrow 6x-4-60=3\left(-2x-11\right)\\ \Leftrightarrow6x-64=-6x-33\\\Leftrightarrow 6x+6x=64-33\\\Leftrightarrow 12x=31\\ \Leftrightarrow x=\frac{31}{12}\)

Vậy nghiệm của phương trình trên là \(\frac{31}{12}\)

Answer 6

https://i.imgur.com/eibeove.jpg

Answer 7

\(d.\frac{7x}{8}-5\left(x-9\right)=\frac{\left(20x+1,5\right)}{6}\\ \Leftrightarrow\frac{21x}{24}-\frac{120\left(x-9\right)}{24}=\frac{4\left(20x+1,5\right)}{24}\\ \Leftrightarrow21x-120x+1080=80x+6\\\Leftrightarrow 21x-120x-80x=-1080+6\\\Leftrightarrow -179x=-1074\\ \Leftrightarrow x=6\)

Vậy nghiệm của phương trình trên là \(6\)

Answer 8

a) Ta có: \(\frac{x-3}{5}=6-\frac{1-2x}{2}\)

\(\Leftrightarrow\frac{x-3}{5}-6+\frac{1-2x}{2}=0\)

\(\Leftrightarrow\frac{2\left(x-3\right)}{10}-\frac{60}{10}+\frac{5\left(1-2x\right)}{10}=0\)

\(\Leftrightarrow2x-6-60+5-10x=0\)

\(\Leftrightarrow-8x-61=0\)

\(\Leftrightarrow-8x=61\)

hay \(x=\frac{-61}{8}\)

Vậy: \(x=\frac{-61}{8}\)

b) Ta có: \(\frac{3x-2}{6}-5=\frac{3-2\left(x+7\right)}{4}\)

\(\Leftrightarrow\frac{3x-2}{6}-5-\frac{3-2\left(x+7\right)}{4}=0\)

\(\Leftrightarrow\frac{2\left(3x-2\right)}{12}-\frac{60}{12}-\frac{3\left(-2x-11\right)}{12}=0\)

\(\Leftrightarrow6x-4-60-3\left(-2x-11\right)=0\)

\(\Leftrightarrow6x-64+6x+33=0\)

\(\Leftrightarrow12x-31=0\)

\(\Leftrightarrow12x=31\)

hay \(x=\frac{31}{12}\)

Vậy: \(x=\frac{31}{12}\)

c) Ta có: \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)

\(\Leftrightarrow2x+\frac{6}{5}=5-\frac{13}{5}-x\)

\(\Leftrightarrow2x+\frac{6}{5}-\frac{12}{5}+x=0\)

\(\Leftrightarrow3x-\frac{6}{5}=0\)

\(\Leftrightarrow3x=\frac{6}{5}\)

hay \(x=\frac{2}{5}\)

Vậy: \(x=\frac{2}{5}\)

d) Ta có: \(\frac{7x}{8}-5\left(x-9\right)=\frac{20x+1.5}{6}\)

\(\Leftrightarrow\frac{7x}{8}-5\left(x-9\right)-\frac{20x+1.5}{6}=0\)

\(\Leftrightarrow\frac{3\cdot7x}{24}-\frac{24\cdot5\cdot\left(x-9\right)}{24}-\frac{4\left(20x+1.5\right)}{24}=0\)

\(\Leftrightarrow21x-120\left(x-9\right)-4\left(20x+1.5\right)=0\)

\(\Leftrightarrow21x-120x+1080-80x-6=0\)

\(\Leftrightarrow-179x+1074=0\)

\(\Leftrightarrow-179x=-1074\)

hay x=6

Vậy: x=6