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Bài 1 :
Ta có :
\(\left|2x-1\right|=5\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-1=5\\2x-1=-5\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=6\\2x=-4\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{6}{2}\\x=\frac{-4}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}}\)
Vậy \(x=-2\) hoặc \(x=3\)
Bài 2 :
Đặt \(A=\frac{3x+4}{x-1}\) ta có :
\(A=\frac{3x+4}{x-1}=\frac{3x-3+7}{x-1}=\frac{3x-3}{x-1}+\frac{7}{x-1}=\frac{3\left(x-1\right)}{x-1}+\frac{7}{x-1}=3+\frac{7}{x-1}\)
Để A là số nguyên thì \(\frac{7}{x-1}\) phải nguyên \(\Rightarrow\)\(7⋮\left(x-1\right)\)\(\Rightarrow\)\(\left(x-1\right)\inƯ\left(7\right)\)
Mà \(Ư\left(7\right)=\left\{1;-1;7;-7\right\}\)
Suy ra :
\(x-1\) | \(1\) | \(-1\) | \(7\) | \(-7\) |
\(x\) | \(2\) | \(0\) | \(8\) | \(-6\) |
Vậy \(x\in\left\{-6;0;2;8\right\}\) thì \(A\inℤ\)
Chúc bạn học tốt ~
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a) b)
(x-140):7=3 720:[41-(2x+5)]=10
x-140=21 41-(2x+5)=72
x=161 2x+5=(-31)
2x=(-36)
x=-18
![](https://rs.olm.vn/images/avt/0.png?1311)
3/4+1/4:x=-3
1/4:x=(-3)-3/4
1/4:x=-15/4
x=-15/4.1/4
x=-15/16
đúng nha bn
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\frac{62}{7}:x=\frac{29}{9}:\frac{3}{56}\)
\(\frac{62}{7}:x=\frac{1624}{27}\)
\(x=\frac{62}{7}:\frac{1624}{27}=\frac{837}{5684}\)
\(b,\frac{1}{5}:x=\frac{1}{5}-\frac{1}{7}\)
\(\frac{1}{5}:x=\frac{2}{35}\)
\(x=\frac{1}{5}:\frac{2}{35}=\frac{7}{2}\)
\(c,\frac{2}{3}.x-\frac{4}{7}=\frac{1}{7}\)
\(\frac{2}{3}.x=\frac{1}{7}+\frac{4}{7}=\frac{5}{7}\)
\(x=\frac{5}{7}:\frac{2}{3}=\frac{15}{14}\)
\(d,\frac{2}{7}-\frac{8}{9}.x=\frac{2}{3}\)
\(\frac{8}{9}.x=\frac{2}{7}-\frac{2}{3}=-\frac{8}{21}\)
\(x=-\frac{8}{21}:\frac{8}{9}=-\frac{3}{7}\)
\(e,\frac{4}{7}+\frac{5}{9}:x=\frac{1}{5}\)
\(\frac{5}{9}:x=\frac{1}{5}-\frac{4}{7}=-\frac{13}{35}\)
\(x=\frac{5}{9}:-\frac{13}{35}=\frac{175}{117}\)
\(i,\frac{2}{5}-\frac{2}{5}.x=\frac{2}{5}\)
\(\frac{2}{5}.\left(1-x\right)=\frac{2}{5}\)
\(1-x=\frac{2}{5}:\frac{2}{5}=1\)
\(x=1-1=0\)
\(g,\frac{2}{3}+\frac{1}{3}:x=-1\)
\(\frac{1}{3}:x=-1-\frac{2}{3}=-\frac{5}{3}\)
\(x=\frac{1}{3}:-\frac{5}{3}=-\frac{1}{5}\)
học tốt nha
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x=\dfrac{4}{27}-\dfrac{2}{3}\)
\(x=-\dfrac{14}{27}\)
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\(5^x-2-3^2=2^4-\left(2^8x2^4-2^{10}x2^2\right)\)
\(5^x-2-3^2=2^4-\left(2^{8+4}-2^{10+2}\right)\)
\(5^x-2-3^2=2^4-\left(2^{12}-2^{12}\right)\)
\(5^x-2-3^2=2^4-0\)
\(5^x-2-3^2=2^4\)
\(5^x-2-9=16\)
\(5^x-2=16+9\)
\(5^x-2=25\)
\(5^x=25+2\)
\(5^x=27\)
Bởi vì 27 không phân tích được 1 số có số mũ là 2
\(\Rightarrow\) Không tồn tại x
\(5^{x-2}-9=16-\left(256.16-1024.4\right)\)
\(\Rightarrow5^{x-2}-9=16-\left(4096-4096\right)\)
\(\Rightarrow5^{x-2}-9=16-0\)
\(\Rightarrow5^{x-2}-9=16\)
\(\Rightarrow5^{x-2}=25\)
\(\Rightarrow x-2=25:5\)
\(\Rightarrow x-2=3\)
\(\Rightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x-2\right)^5-\left(x-2\right)^3=0\)
\(\Rightarrow\left(x-2\right)^3\left(\left(x-2\right)^2-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^2-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\\left(x-2\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=1\\x-2=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{1;2;3\right\}\)
⇒ ( x - 2)3 . (x - 2)2 - (x - 2)3 . 1 = 0 ⇒ ( x - 2)3 . [( x - 2)2 - 1] = 0
![](https://rs.olm.vn/images/avt/0.png?1311)
Lâu rồi mình ko giải, sai thì thôi nhé!
a) \(\left(10-2x\right)^2=25-\left(-11\right)\)'=
\(\Leftrightarrow\left(10-2x\right)^2=36\)
\(\Leftrightarrow\left(10-2x\right)^2=6^2\)
\(\Leftrightarrow\orbr{\begin{cases}10-2x=6\\10-2x=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=10-6\\2x=10-\left(-6\right)\end{cases}\Leftrightarrow}\orbr{\begin{cases}2x=4\\2x=16\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=2\\x=8\end{cases}}}\)
Vậy \(x\in\left\{2;8\right\}\)
b) \(-2\left(-x+5\right)-3\left(5-x\right)=4\left(2+x\right)\)
\(\Leftrightarrow-2\left(5-x\right)-3\left(5-x\right)=4\left(2+x\right)\)
\(\Leftrightarrow-5\left(5-x\right)=4\left(2+x\right)\)
\(\Leftrightarrow-25+5x=8+4x\)
\(\Leftrightarrow5x-25=8+4x\)
\(\Leftrightarrow5x=8+4x+25\)
\(\Leftrightarrow5x=4x+33\)
\(\Leftrightarrow5x-4x=33\)
\(\Leftrightarrow1x=33\)
\(\Leftrightarrow x=33\)
Vậy \(x=33\)
a) (10 - 2x)2 = 25 - (-11)
(10 - 2x)2 = 36
(10 - 2x)2 = 62
=> 10 - 2x = 6
2x = 10 - 6
2x = 4
x =4:2
x=2
Vậy x = 2
b)-2(-x+5) - 3(5 - x) = 4(2+x)
2x - 10 - 15 +3x = 8 + 4x
2x - 25 + 3x = 8 +4x
2x + 3x - 4x = 8 + 25
5x - 4x = 33
x= 33
Vậy x = 33
2x-6-3x+15=12-4x-18
-x+9=-6-4x
-x+4x=-9-6
3x=-15
x=-5
trước đó có dấu tương đương hay suy ra cũng được
2 . ( x - 3 ) - 3 . ( x - 5 ) = 4 , ( 3 - x ) - 18
2x - 2 . 3 - 3x + 3 . 5 = 4 . 3 - 4x - 18
2x - 6 - 3x + 15 = 12 - 4x - 18
2x - 3x + 4x = 12 - 18 + 6
3x = 0
=> x = 0
Học tốt nhé bạn !