tìm x: a, 1/3 +2/3 x = 1/4 b, l 3x +1 l -17 = -12
mn giúp mk vs nha
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a)\(\left(4x+1\right)\left(x-3\right)-\left(x-7\right)\left(4x-1\right)=15\)
\(4x^2-11x-3-\left(4x^2-29x+7\right)=15\)
\(4x^2-11x-3-4x^2+29x-7=15\)
\(18x-10=15\)
\(x=\frac{25}{18}\)
b)\(\left(3x-5\right)\left(x+1\right)-\left(3x-1\right)\left(x+1\right)=x-4\)
\(\left(x+1\right)\left(3x-5-3x+1\right)=x-4\)
\(\left(x+1\right).\left(-4\right)-x+4=0\)
\(-4x-4-x+4=0\)
\(x=0\)
1.a) ĐK : \(3-2x\ge0\forall x\Rightarrow x\le\frac{3}{2}\)
Khi đó : \(\left|\frac{1}{2}x\right|=3-2x\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=3-2x\\\frac{1}{2}x=-3+2x\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{5}{2}x=3\\\frac{3}{2}x=3\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{6}{5}\\x=2\end{cases}}\left(tm\right)\)
Vậy \(x\in\left\{\frac{6}{5};2\right\}\)
b) ĐK : \(3x+2\ge0\Rightarrow x\ge\frac{-2}{3}\)
Khi đó : \(\left|x-1\right|=3x+2\Leftrightarrow\orbr{\begin{cases}x-1=3x+2\\x-1=-3x-2\end{cases}}\Rightarrow\orbr{\begin{cases}-2x=3\\4x=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1,5\\x=-0,25\left(tm\right)\end{cases}}\)
Vậy x = -0,25
c) ĐKXĐ : \(x-12\ge0\Rightarrow x\ge12\)
Khi đó |5x| = x - 12
<=> \(\orbr{\begin{cases}5x=x-12\\5x=-x+12\end{cases}}\Rightarrow\orbr{\begin{cases}4x=-12\\6x=12\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=2\end{cases}}\left(\text{loại}\right)\)
Vậy \(x\in\varnothing\)
d) ĐK : \(5x+1\ge0\Rightarrow x\ge-\frac{1}{5}\)
Khi đó \(\left|17-x\right|=5x+1\Leftrightarrow\orbr{\begin{cases}17-x=5x+1\\17-x=-5x-1\end{cases}}\Rightarrow\orbr{\begin{cases}6x=16\\-4x=18\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{8}{3}\left(tm\right)\\x=-4,5\left(\text{loại}\right)\end{cases}}\)
Vậy x = 8/3
Tóm lại : Cách làm là
|f(x)| = g(x)
ĐK : g(x) \(\ge0\)
=> \(\orbr{\begin{cases}f\left(x\right)=-g\left(x\right)\\f\left(x\right)=g\left(x\right)\end{cases}}\)
Bạn tự làm tiếp đi ak
\(\left|2x-\frac{1}{2}\right|+1=3x\)
\(\Leftrightarrow\left|2x-\frac{1}{2}\right|=3x-1\)
\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{1}{2}=3x-1\\2x-\frac{1}{2}=1-3x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-3x=-1+\frac{1}{2}\\2x+3x=1+\frac{1}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}-x=-\frac{1}{2}\\5x=\frac{3}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{3}{10}\end{cases}}\)
a)\(\frac{1}{3}+\frac{2}{3}x=\frac{1}{4}\)
\(\Rightarrow\frac{2}{3}x=\frac{1}{4}-\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}x=-\frac{1}{12}\)
\(\Rightarrow x=-\frac{1}{12}:\frac{2}{3}\)
\(\Rightarrow x=-\frac{1}{8}\)
b)\(\left|3x+1\right|-17=-12\)
\(\Rightarrow\left|3x+1\right|=5\)
\(\Rightarrow\orbr{\begin{cases}3x+1=5\\3x+1=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=4\\3x=-6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=-2\end{cases}}\)
a, 1/3 \(+\)2/3 x \(=\)1/4
\(\Rightarrow\)2/3x \(=\)1/4 \(-\)1/3
\(\Rightarrow\)2/3 x \(=\)\(\frac{-1}{12}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{12}\)\(\div\)\(\frac{2}{3}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{12}\)\(\times\)\(\frac{2}{3}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{18}\)
b, \(|\)3x \(+\)1\(|\)\(-\)17 \(=\)-12
\(\Rightarrow\)\(|\)3x \(+\)1\(|\)\(=\)-12 \(+\)17
\(\Rightarrow\)\(|\)3x \(+\)1\(|\)\(=\)5
\(\Rightarrow\)3x \(+\)1 \(=\)5 ; 3x \(+\)1\(=\)-5
\(\Rightarrow\)3x \(=\)5 \(-\)1 ; 3x \(=\)-5 \(-\)1
\(\Rightarrow\)3x \(=\)4 ; 3x \(=\)-6
\(\Rightarrow\)x \(=\)4 : 3 ; x \(=\)-6 : 3
\(\Rightarrow\)x \(=\)\(\frac{4}{3}\); x \(=\)-2