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a, \(\left|x-3\right|-2\left(-4\right)=\left(-7\right)\left(-12\right)\)
\(\Leftrightarrow\left|x-3\right|+8=84\Leftrightarrow\left|x-3\right|=76\Leftrightarrow x-3=\pm76\)
TH1 : \(x-3=76\Leftrightarrow x=79\)
TH2 : \(x-3=-76\Leftrightarrow x=-73\)
b, \(\left|x+2\right|+3=3^3=27\Leftrightarrow\left|x+2\right|=24\Leftrightarrow x+2=\pm24\)
TH1 : \(x+2=24\Leftrightarrow x=22\)
TH2 : \(x+2=-24\Leftrightarrow x=-26\)
3, \(x-5⋮x-1\)
\(x-1-4⋮x-1\)
\(-4⋮x-1\Rightarrow x-1\inƯ\left(-4\right)=\left\{\pm1;\pm4\right\}\)
| x - 1 | 1 | -1 | 4 | -4 |
| x | 2 | 0 | 5 | -3 |
4,\(3x+5⋮2x-1\Leftrightarrow6x+10⋮2x+1\)
\(\Leftrightarrow3\left(2x+1\right)+7⋮2x+1\Leftrightarrow7⋮2x+1\)
\(\Rightarrow2x+1\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
| 2x + 1 | 1 | -1 | 7 | -7 |
| 2x | 0 | -2 | 6 | -8 |
| x | 0 | -1 | 3 | -4 |
a) \(x\cdot x^2\cdot x^3\cdot x^4=1024\)
\(x^{1+2+3+4}=1024\)
\(x^{10}=1024\)
\(x^{10}=2^{10}\)
\(\Rightarrow x=2\)
b) \(\left(x+5\right)\cdot2^3-2^2\cdot5=2^2\cdot3\cdot5\)
\(2^2\cdot\left[2\left(x+5\right)-5\right]=2^2\cdot15\)
\(2^2\cdot\left[2x+10-5\right]=2^2\cdot15\)
\(2^2\cdot\left[2x+5\right]=2^2\cdot15\)
\(\Rightarrow2x+5=15\)
\(\Rightarrow2x=15+5=20\)
\(\Rightarrow x=\frac{20}{2}=10\)
a)\(x.x^2.x^3.x^4=1024\Rightarrow x^{1+2+3+4}=2^{10}\Rightarrow x^{10}=2^{10}\Rightarrow x=2\)
b)\(\left(x+5\right).2^3-2^2.5=2^2.3.5\Rightarrow\left(x+5\right).2^3=2^2.3.5+2^2.5\)
\(\Rightarrow\left(x+5\right).2^3=2^2.5.\left(3+1\right)=2^2.5.2^2=2^4.5\)
\(\Rightarrow x+5=\frac{2^4.5}{2^3}=10\Rightarrow x=5\)
+) Ta có: \(15-x+17=-\left(-6\right)+\left|-12\right|\)
\(\Leftrightarrow-x+32=6+12\)
\(\Leftrightarrow-x=18-32\)
\(\Leftrightarrow x=14\)
Vậy......
+) Ta có: \(x+20=-\left(-23\right)\)
\(\Leftrightarrow x+20=23\)
\(\Leftrightarrow x=3\)
Vậy........
+) Ta có: \(-\left|-5\right|-\left(-x\right)+4=3-\left(-25\right)\)
\(\Leftrightarrow-5+x+4=3+25\)
\(\Leftrightarrow x=29\)
Vậy.....
Chúc e hok tốt và giữ lời hứa nhá ^_^
\(3^{2x+2}=9^{x+3}\)
=) \(3^{2x+2}=\left(3^2\right)^{x+3}=3^{2x+6}\)
=) \(2x+2=2x+6\)
=) \(2x=2x+6-2=2x+4\)
=) \(2x-2x=4\)=) \(0=4\)( Vô lý vì \(0\ne4\))
=) Không tìm được x
\(\Leftrightarrow3^x=5.3^{12}+4.\left(3^3\right)^4=5.3^{12}+4.3^{12}.\)
\(\Leftrightarrow3^x=9.3^{12}=3^2.3^{12}=3^{14}\Leftrightarrow x=14\)
a, \(3-\left|2x+1\right|=\left(-5\right)\Leftrightarrow\left|2x+1\right|=8\Leftrightarrow2x+1=\pm8\)
TH1 : \(2x+1=8\Leftrightarrow x=\frac{7}{2}\)
TH2 : \(2x+1=-8\Leftrightarrow x=-\frac{9}{2}\)
b, \(12+\left|3-x\right|=9\Leftrightarrow\left|3-x\right|=3\Leftrightarrow3-x=\pm3\)
TH1 : \(3-x=3\Leftrightarrow x=0\)
TH2 : \(3-x=-3\Leftrightarrow x=6\)
a,3- | 2x + 1 | = ( - 5 )
| 2x + 1 | = 8
TH1: 2x+1=8
2x=7
x=7/2
TH2:2x+1=-8
2x=-9
x=-9/2
| x-3 | -2 . (-4) = (-7).(-12)
|x-3| - (-8 ) = 84
|x-3| +8 = 84
=> |x-3| = 84-8
=> |x-3| = 76
\(\Leftrightarrow\orbr{\begin{cases}x-3=76\\x-3=-76\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=76+3\\x=-76+3\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=79\\x=-73\end{cases}}\)
Vậy x\(\in\left\{79;-73\right\}\)
b, | x+2| +3 = 33
|x+2| +3 = 27
|x+2|= 27-3
|x+2|=24
\(\Leftrightarrow\orbr{\begin{cases}x+2=24\\x+2=-24\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=24-2\\x=-24-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=22\\x=-26\end{cases}}}\)
Vậy x\(\in\) {22;-26}
|x - 3| - 2 . (- 4) = (- 7) . (- 12)
\(\Leftrightarrow\)|x - 3| + 8 = 84
\(\Leftrightarrow\)|x - 3| = 76
\(\Rightarrow\orbr{\begin{cases}x-3=76\\x-3=-76\end{cases}\Rightarrow\orbr{\begin{cases}x=79\\x=-73\end{cases}}}\)
Vậy x = 76 hoặc x = - 73