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a) (3x-1)3 = 27 = 33
=> 3x - 1 = 3
3x = 4
x = 4/3
b) 32x-1 = 27 = 33
=> 2x - 1 = 3
2x = 4
x = 2
c) 68-2x = 36 = 62
=> 8 -2x = 2
=> 2x = 6
x = 3
d) (3x-2)10 = (3x-2)7
=> (3x-2)10 - (3x-2)7 = 0
(3x-2)7. [(3x-2)3 - 1] = 0
=> (3x-2)7 = 0 => 3x-2 = 0 => 3x = 2 => x = 2/3
(3x-2)3 - 1 = 0 => (3x-2)3 = 1 => 3x - 2 = 1 => 3x = 3 => x = 1
KL:...
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\(\left(2x+3\right)^2=\frac{9}{121}\)
\(\left(2x+3\right)^2=\left(\frac{3}{11}\right)^2\)
\(\Rightarrow2x+3=\frac{3}{11}\text{ hoặc }2x+3=\frac{-3}{11}\)
\(2x=\frac{3}{11}-3\text{ hoặc }2x=\frac{-3}{11}-3\)
\(2x=\frac{3}{11}-\frac{33}{11}\text{ hoặc }2x=\frac{-3}{11}-\frac{33}{11}\)
\(2x=\frac{-30}{11}\text{ hoặc }2x=\frac{-36}{11}\)
\(x=\frac{-30}{11}:2\text{ hoặc }x=\frac{-36}{11}:2\)
\(x=\frac{-30}{11}.\frac{1}{2}\text{ hoặc }x=\frac{-36}{11}.\frac{1}{2}\)
\(x=\frac{-15}{11}\text{ hoặc }x=\frac{-18}{11}\)
1. 3x - 9 = (-1) - x
=> 3x + x = (-1) + 9
=> 4x = 8
=> x = 8 : 4
=> x = 2
2. 2x - 23 = 17 - 3x
=> 2x - 8 = 17 - 3x
=> 2x + 3x = 17 + 8
=> 5x = 25
=> x = 25 : 5
=> x = 5
3. |x - 3| + 8 = 12
=> |x - 3| = 12 - 8
=> |x - 3| = 4
=> \(\orbr{\begin{cases}x-3=4\\x-3=-4\end{cases}}\)
=> \(\orbr{\begin{cases}x=4+3\\x=-4+3\end{cases}}\)
=> \(\orbr{\begin{cases}x=7\\x=-1\end{cases}}\)
4. 12 - 2|x| = |-2012|
=> 12 - 2|x| = 2012
=> 2|x| = 12 - 2012
=> 2|x| = -2000
=> |x| = -2000 : 2
=> |x| = -1000
=> x không có số nào thỏa mãn
5. 19 - (14 + 19) = x - (27 - 9)
=> 19 - 14 - 19 = x - 18
=> -14 = x - 18
=> x - 18 = -14
=> x = -14 + 18
=> x = 4
6. 15 - |x - 3| = 2
=> |x - 3| = 15 - 2
=> |x - 3| = 13
=> \(\orbr{\begin{cases}x-3=13\\x-3=-13\end{cases}}\)
=> \(\orbr{\begin{cases}x=13+3\\x=-13+3\end{cases}}\)
=> \(\orbr{\begin{cases}x=16\\x=10\end{cases}}\)
7. |x - 5| - 27 = -6
=> |x - 5| = -6 + 27
=> |x - 5| = 21
=> \(\orbr{\begin{cases}x-5=21\\x-5=-21\end{cases}}\)
=> \(\orbr{\begin{cases}x=21+5\\x=-21+5\end{cases}}\)
=> \(\orbr{\begin{cases}x=26\\x=-16\end{cases}}\)
8. 3 . |x - 2| = |-15|
=> 3 . |x - 2| = 15
=> |x - 2| = 15 : 3
=> |x - 2| = 5
=> \(\orbr{\begin{cases}x-2=5\\x-2=-5\end{cases}}\)
=> \(\orbr{\begin{cases}x=5+2\\x=-5+2\end{cases}}\)
=> \(\orbr{\begin{cases}x=7\\x=-3\end{cases}}\)
9. 11 - 2|x| = -3
=> 2|x| = 11 - (-3)
=> 2|x| = 14
=> |x| = 14 : 2
=> |x| = 7
=> \(\orbr{\begin{cases}x=7\\x=-7\end{cases}}\)
10.|x - 2| = 1
=> \(\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=1+2\\x=-1+2\end{cases}}\)
=> \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(a,\Rightarrow x=3\\ b,\Rightarrow2x-1=2\Rightarrow x=\dfrac{3}{2}\\ c,\Rightarrow\left[{}\begin{matrix}x-2=4\\x-2=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\\ d,\Rightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\\ e,\Rightarrow2x+5=3^2=9\Rightarrow x=2\)
\(a)\frac{5}{8}-x=2\frac{1}{6}\)
\(\Rightarrow\frac{5}{8}-x=\frac{13}{6}\)
\(\Rightarrow x=\frac{5}{8}-\frac{13}{6}\)
\(\Rightarrow x=\frac{15}{24}-\frac{52}{24}\)
\(\Rightarrow x=-\frac{37}{24}\)
\(b)\) \(\frac{4}{9}:x=-\frac{1}{3}+1\frac{1}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{1}{3}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{2}{6}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}:\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}.\frac{6}{5}\)
\(\Rightarrow x=\frac{8}{15}\)
\(c)\left(3x-2\right)^3=-\frac{1}{27}\)
\(\Rightarrow3x-2=-\frac{1}{3}\)
\(\Rightarrow3x=-\frac{1}{3}+2\)
\(\Rightarrow3x=-\frac{1}{3}+\frac{6}{3}\)
\(\Rightarrow3x=\frac{5}{3}\)
\(\Rightarrow x=\frac{5}{3}:3\)
\(\Rightarrow x=\frac{5}{9}\)
d ) và e ) tự làm
Chúc bạn học tốt !!!
\(\Leftrightarrow3x-1=-\dfrac{2}{3}\)
hay x=1/9
\(\Rightarrow3x-1=-\dfrac{2}{3}\Rightarrow3x=\dfrac{1}{3}\Rightarrow x=\dfrac{1}{9}\)