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a) | \(\frac{1}{2}\)x| = 3 - 2x
\(\Rightarrow\orbr{\begin{cases}\frac{1}{2}x=3-2x\\\frac{1}{2}x=-\left(3-2x\right)\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{1}{2}x+2x=3\\\frac{1}{2}x=-3+2x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}\frac{5}{2}x=3\\\frac{1}{2}x-2x=-3\end{cases}}\Rightarrow\orbr{\begin{cases}x=3:\frac{5}{2}\\-\frac{3}{2}x=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{6}{5}\\x=-3:\left(-\frac{3}{2}\right)\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{6}{5}\\x=2\end{cases}}\)
b) |x - 1| = 3x + 2
\(\Rightarrow\orbr{\begin{cases}x-1=3x+2\\x-1=-\left(3x+2\right)\end{cases}}\Rightarrow\orbr{\begin{cases}x-3x=2+1\\x-1=-3x-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-2x=3\\x+3x=-2+1\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{3}{-2}\\4x=-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=-\frac{1}{4}\end{cases}}\)
c) | 5x | = x - 12
\(\Rightarrow\orbr{\begin{cases}5x=x-12\\5x=-\left(x-12\right)\end{cases}}\Rightarrow\orbr{\begin{cases}5x-x=-12\\5x=-x+12\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}4x=-12\\5x+x=12\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\6x=12\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=2\end{cases}}\)
d) |7 - x| = 5x + 1
\(\Rightarrow\orbr{\begin{cases}7-x=5x+1\\7-x=-\left(5x+1\right)\end{cases}}\Rightarrow\orbr{\begin{cases}7-1=5x+x\\7-x=-5x-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}6=6x\\7+1=-5x+x\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\8=-4x\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-2\end{cases}}\)
e) |9 + x| = 2x
\(\Rightarrow\orbr{\begin{cases}9+x=2x\\9+x=-2x\end{cases}}\Rightarrow\orbr{\begin{cases}9=2x-x\\9=-2x-x\end{cases}}\Rightarrow\orbr{\begin{cases}9=x\\9=-3x\end{cases}}\Rightarrow\orbr{\begin{cases}x=9\\x=-3\end{cases}}\)
Ủng hộ mk nha !!! ^_^
\(5-\left|3x-1\right|=3\)
\(\left|3x-1\right|=2\)
\(\Rightarrow\orbr{\begin{cases}3x-1=2\\3x-1=-2\end{cases}}\Rightarrow\orbr{\begin{cases}3x=3\\3x=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=\frac{-1}{3}\end{cases}}\)
vậy \(\orbr{\begin{cases}x=1\\x=\frac{-1}{3}\end{cases}}\)
\(\left|x+\frac{3}{4}\right|-5=-2\)
\(\left|x+\frac{3}{4}\right|=3\)
\(\Rightarrow\orbr{\begin{cases}x+\frac{3}{4}=3\\x+\frac{3}{4}=-3\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{9}{4}\\x=-\frac{15}{4}\end{cases}}\)
\(\left(1-2x\right)^2=9\)
\(\left(1-2x\right)^2=3^2\)
\(\Rightarrow1-2x=3\)
\(\Rightarrow2x=-2\)
\(\Rightarrow x=-1\)
vậy \(x=-1\)
\(\left(x+5\right)^3=-64\)
\(\left(x+5\right)^3=\left(-4\right)^3\)
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=-9\)
vậy \(x=-9\)
\(\left(2x+1\right)^2=\frac{4}{9}\)
\(\left(2x+1\right)^2=\left(\frac{2}{3}\right)^2\)
\(\Rightarrow2x+1=\frac{2}{3}\)
\(\Rightarrow2x=\frac{-1}{3}\)
\(\Rightarrow x=\frac{-1}{6}\)
vậy \(x=-\frac{1}{6}\)
a, 2x-3-x+5=x+2-x+1
2x-x-x+x=2+1+3-5
0x=1
=> x thuộc rỗng (vì số nào nhân với 0 cũng bằng 0)
b, 2x-2-5x+10=-10
2x-5x=-10+2-10
-3x=2
x=-2/3
c, 2x-10-3x+21=14
2x-3x=14+10-21
-x=3
x=-3
d, 5x-6-2x+6=12
5x-2x=12+6-6
3x=12
x=4
e, -35+7x-2x+10=15
7x-2x=15+35-10
5x=40
x=8
\(c)\) \(\left|2x-1\right|-2x=3\)
\(\Leftrightarrow\)\(\left|2x-1\right|=2x+3\)
Ta có : \(\left|2x-1\right|\ge0\)
\(\Rightarrow\)\(2x+3\ge0\)\(\Rightarrow\)\(2x\ge-3\)\(\Rightarrow\)\(x\ge\frac{-3}{2}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-1=2x+3\\2x-1=-2x-3\end{cases}\Leftrightarrow\orbr{\begin{cases}2x-2x=3+1\\2x+2x=-3+1\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}0=4\\4x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}0=4\left(loai\right)\\x=\frac{-1}{2}\left(tm\right)\end{cases}}}\)
Vậy \(x=\frac{-1}{2}\)
Chúc bạn học tốt ~
\(b)\) \(3\left(2x-1\right)-\left|x-5\right|=7\)
\(\Leftrightarrow\)\(3\left(2x-1\right)-7=\left|x-5\right|\)
\(\Leftrightarrow\)\(6x-3-7=\left|x-5\right|\)
\(\Leftrightarrow\)\(\left|x-5\right|=6x-10\)
Ta có : \(\left|x-5\right|\ge0\)
\(\Rightarrow\)\(6x-10\ge0\)\(\Rightarrow\)\(6x\ge10\)\(\Rightarrow\)\(x\ge\frac{5}{3}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x-5=6x-10\\x-5=10-6x\end{cases}\Leftrightarrow\orbr{\begin{cases}6x-x=-5+10\\x+6x=10+5\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}5x=5\\7x=15\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\left(loai\right)\\x=\frac{15}{7}\left(tm\right)\end{cases}}}\)
Vậy \(x=\frac{15}{7}\)
Chúc bạn học tốt ~
