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\(a,\frac{1}{2}x+\frac{5}{2}=\frac{7}{2}x-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x+\frac{5}{2}-\frac{7}{2}x=-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{7}{2}x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x=-\frac{13}{4}\)
\(\Leftrightarrow x=-\frac{13}{4}:(-3)=-\frac{13}{4}:\frac{-3}{1}=-\frac{13}{4}\cdot\frac{-1}{3}=\frac{13}{12}\)
\(b,\frac{2}{3}x-\frac{2}{5}=\frac{1}{2}x-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{2}{5}-\frac{1}{2}x=-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{1}{2}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x=\frac{1}{15}\)
\(\Leftrightarrow x=\frac{1}{15}:\frac{1}{6}=\frac{1}{15}\cdot6=\frac{6}{15}=\frac{2}{5}\)
\(c,\frac{1}{3}x+\frac{2}{5}(x+1)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)
\(\Leftrightarrow\frac{11}{15}x=-\frac{2}{5}\)
\(\Leftrightarrow x=-\frac{6}{11}\)
d,e,f Tương tự
a) \(\left(\frac{1}{7}x-\frac{2}{3}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\frac{1}{7}x-\frac{2}{3}=0\\-\frac{1}{5}x+\frac{3}{5}=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}\frac{1}{7}x=\frac{2}{3}\\-\frac{1}{5}x=-\frac{3}{5}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{14}{3}\\x=3\end{cases}}\)
b)\(\frac{1}{10}x-\frac{4}{5}x+1=0\)
\(\Leftrightarrow x.\left(\frac{1}{10}-\frac{4}{5}\right)+1=0\)
\(\Rightarrow-\frac{7}{10}x=-1\)
\(\Rightarrow x=\frac{10}{7}\)
c)\(\left(2x-\frac{1}{3}\right).\left(5x+\frac{2}{7}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-\frac{1}{3}=0\\5x+\frac{2}{7}=0\end{cases}\Rightarrow\orbr{\begin{cases}2x=\frac{1}{3}\\5x=-\frac{2}{7}\end{cases}}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{6}\\x=-\frac{2}{35}\end{cases}}\)
a, (1/7 . x - 2/3) . (-1/5 . x + 3/5) = 0
Suy ra : 1/7 .x -2/3 = 0 hoặc -1/5 .x + 3/5 =0
Vậy : 1/7 .x = 2/3 hoặc -1/5 .x = 3/5
x =2/3 : 1/7 hoặc x = 3/5 : (-1/5)
x = 14/3 hoặc x = -3
b, 1/10 .x - 4/5 .x + 1 =0
x . (1/10 - 4/5) + 1 = 0
x . (-7/10) + 1 = 0
x . -7/10 =0 +1 = 1
x = 1 : (-7/10)
x = -10/7
c, (2x - 1/3 ) . (5x +2/7) = 0
Suy ra : 2x - 1/3 = 0 hoặc 5x + 2/7 = 0
Vậy : 2x = 1/3 hoặc 5x = 2/7
x = 1/3 : 2 hoặc x = 2/7 : 5
x = 1/6 hoặc x = 2/35
a) |2x-3|+x=21
|2x-3|=21-x
\(\Rightarrow\)\(\orbr{\begin{cases}2x-3=21-x\\2x-3=-\left(21-x\right)\end{cases}}\)
TH1: 2x-3=21-x
2x-x=21+3
x=24
TH2: 2x-3=-(21-x)
2x-3 = -21+x
2x-x=-21+3
x=-18
Vậy x \(\varepsilon\){-18;24}
a) \(\dfrac{x}{x+1}=\dfrac{x+5}{x+7}\)
\(\Leftrightarrow x\left(x+7\right)=\left(x+1\right)\left(x+5\right)\)
\(\Leftrightarrow x^2+7x=\left(x+1\right)x+\left(x+1\right).5\)
\(\Leftrightarrow x^2+7x=x^2+x+5x+5\)
\(\Leftrightarrow x^2+7x=x^2+6x+5\)
\(\Leftrightarrow x^2+7x-6x-x^2=5\)
\(\Leftrightarrow x=5\)
Vậy...
b) \(\dfrac{x+7}{x+4}=\dfrac{x-1}{x-2}\)
\(\Leftrightarrow\left(x+7\right)\left(x-2\right)=\left(x+4\right)\left(x-1\right)\)
\(\Leftrightarrow\left(x+7\right)x-\left(x+7\right).2=\left(x+4\right)x-\left(x+4\right)\)
\(\Leftrightarrow x^2+7x-2x+14=x^2+4x-x-4\)
\(\Leftrightarrow x^2+5x+14=x^2+3x-4\)
\(\Leftrightarrow x^2+5x+14-3x-x^2=-4\)
\(\Leftrightarrow2x+14=-4\)
\(\Leftrightarrow2x=-18\)
\(\Leftrightarrow x=-9\)
Vậy...
c) \(\dfrac{x+2}{x-2}=\dfrac{x-3}{x+3}\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=\left(x-2\right)\left(x-3\right)\)
\(\Leftrightarrow\left(x+2\right)x+\left(x+2\right).3=\left(x-2\right)x-\left(x-2\right).3\)
\(\Leftrightarrow x^2+2x+3x+6=x^2-2x-3x+6\)
\(\Leftrightarrow x^2+5x+6=x^2-5x+6\)
\(\Leftrightarrow x^2+5x+6-6+5x-x^2=0\)
\(\Leftrightarrow10x=0\)
\(\Leftrightarrow x=0\)
Vậy...