a) \(\frac{x-1}{6}=\frac{2x+3}{7}\)
\(\Leftrightarrow7\left(x-1\right)=6\left(2x+3\right)\)
\(\Leftrightarrow7x-7=12x+18\)
\(\Leftrightarrow5x+18=-7\)
\(\Leftrightarrow5x=-25\)
\(\Leftrightarrow x=-5\)
b) \(\left(2x^2-\frac{1}{2}x\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow x\left(2x-\frac{1}{2}\right)\left(x^2+1\right)=0\)
Vì \(x^2+1>0\)nên \(\orbr{\begin{cases}x=0\\2x-\frac{1}{2}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{4}\end{cases}}\)
c) \(\frac{4}{3}-\frac{1}{3}\left|x-1\right|=\frac{1}{2}\)
=> \(\frac{1}{3}\left|x-1\right|=\frac{4}{3}-\frac{1}{2}\)
=> \(\frac{1}{3}\left|x-1\right|=\frac{5}{6}\)
=> \(\left|x-1\right|=\frac{5}{6}:\frac{1}{3}\)
=> \(\left|x-1\right|=\frac{5}{2}\)
=> \(\orbr{\begin{cases}x-1=\frac{5}{2}\\x-1=-\frac{5}{2}\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{3}{2}\end{cases}}\)
c) \(\frac{4}{3}-\frac{1}{3}\left|x-1\right|=\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{3}\left|x-1\right|=\frac{4}{3}-\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{3}\left|x-1\right|=\frac{8}{6}-\frac{3}{6}\)
\(\Leftrightarrow\frac{1}{3}\left|x-1\right|=\frac{5}{6}\)
\(\Leftrightarrow\left|x-1\right|=\frac{15}{6}\)
\(\Leftrightarrow\left|x-1\right|=\frac{5}{2}\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=\frac{5}{2}\\x-1=\frac{-5}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=\frac{-3}{2}\end{cases}}\)
a) x - 1/6 = 2x + 3/7
<=> (x - 1).2x = 6.(2x + 3)
<=> 7x - 7 = 12x + 18
<=> 7x = 12x + 18 + 7
<=> 7x = 12x + 25
<=> 7x - 12 = 25
<=> -5x = 25
<=> x = -5
=> x = -5
b) (2x2 - 1/2x)(x2 + 1) = 0
<=> x.(x2 + 1)(2x - 1/2) = 0
x = 0 hoặc 2x - 1/2 = 0
2x = 0 + 1/2
2x = 1/2
x = 1/4
=> x = 0 hoặc x = 1/4
c) 4/3 - 1/3|x - 1| = 1/2
<=> -1/3|x - 1| = 1/2 - 4/3
<=> -1/3|x - 1| = -5/6
<=> |x - 1| = (-5/6) : (-1/3)
<=> |x - 1| = 5/2
<=> x - 1 = 5/2 hoặc x - 1 = -5/2
x = 5/2 + 1 x = -5/2 + 1
x = 7/2 x = -3/2
=> x = 7/2 hoặc x = -3/2
