3/4.(x-1/2)-5/6 =1/3
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`3xx(x-1/6)-2xx(x-1/3)=2/3`
`3x-1/2-2x+2/3=2/3`
`x=2/3-2/3+1/2`
`x=1/2`
`3x(x-1/6)-2x(x-1/3)=2/3`
`3x^2 - 1/2 x- 2x^2 + 2/3x = 2/3`
`x^2+1/6 x =2/3`
`x=(-1 \pm \sqrt97)/12`
\(\frac{\left(\frac{2}{3}\right)^3\cdot\left(-\frac{3}{4}\right)^2\cdot\left(-1\right)^5}{\left(\frac{2}{5}\right)^2\cdot\left(-\frac{5}{12}\right)^3}\)
\(=\frac{\frac{2^3}{3^3}\cdot\frac{3^2}{4^2}\cdot\left(-1\right)}{\frac{2^2}{5^2}\cdot\frac{\left(-5\right)^3}{12^3}}\)
\(=\frac{\frac{8}{27}\cdot\frac{9}{16}\cdot\left(-1\right)}{\frac{4}{25}\cdot\frac{-125}{1728}}=\frac{-\frac{1}{6}}{-\frac{5}{432}}=\left(-\frac{1}{6}\right)\cdot\left(-\frac{432}{5}\right)=\frac{72}{5}\)
\(\dfrac{2x+1}{3}-\dfrac{x-1}{2}< 3\)
\(\Leftrightarrow\dfrac{2\left(2x+1\right)-3\left(x-1\right)}{6}< \dfrac{18}{6}\)
\(\Leftrightarrow2\left(2x+1\right)-3\left(x-1\right)< 18\)
\(\Leftrightarrow4x+2-3x+3< 18\)
\(\Leftrightarrow x< 13\)
Vậy \(S=\left\{x|x< 13\right\}\)
1. (-1) + (-2) + (-3) + ... + (-1999)
= ( (-1999) - (-1) ) : 1 + 1
= ( (-1999) + (-1) ) . (-1997) : 2
=1 997 000
2. 1 +(-2) + 3 + (-4) + ... + 1998 + (-1999)
= ( (-1999) - 1 ) :1 + 1
= ( (-1999) + 1 ) . (-1999) : 2
= 1 997 001
k hộ mik nha""
1. \(\frac{x-3}{x+2}=\frac{3}{4}\)
=> \(4(x-3)=3(x+2)\)
=> 4x - 12 = 3x + 6
=> 4x - 12 - 3x = 6
=> 4x - 3x - 12 = 6
=> x = 18
2. \(\frac{4-x}{x-1}=\frac{-5}{6}\)
=> 6[4 - x] = -5[x - 1]
=> 24 - 6x = 5 - 5x
=> 24 - 6x - 5 = 5x
=> 24 - 5 = 6x - 5x
=> 19 = x
=> x = 19
3. \(\frac{3-x}{-x+2}=\frac{-1}{3}\)
=> 3[3 - x] = -1[-x + 2]
=> 9 - 3x = x - 2
=> 9 - 3x + x = -2
=> 9 - 4x = -2
=> 4x = 9 - [ -2]
=> 4x = 9 + 2 = 11
=> x = 11/4
4. \(\frac{x-1}{12}=\frac{-3}{1-x}\)
=> [x-1][1-x] = -36
=> -[x-1]2 = -36
=> [x-1]2 = 36
=> [x-1]2 = 62
=> x -1 = 6 hoặc x - 1 = -6
=> x = 7 hoặc x = -5
5 . |x - 3 | - 8 = -4
=> |x - 3| = -4 + 8
=> |x - 3| = 4
=> x - 3 = 4 hoặc x - 3 = -4
=> x = 7 hoặc x = -1
Mấy bài sau tương tự
câu a+b dùng quy tắc chuyển vế
c, 3.(1/2-x)-5.(x-1/10)=-7/4
=>(3.1/2-3x)-(5x-5.1/10)=-7/4
=>3/2-3x-5x+1/2=-7/4
=>(3/2+1/2)-(3x+5x)=-7/4
=> 2-8x=-7/4
=>8x=15/4
=>x=15/4:8
=>x=15/32
a) 2.(1/4 - 3x) = 1/5 - 4x
=> 1/2 - 6x = 1/5 -4x
=> -6x + 4x = 1/5 - 1/2
=> -2x = -3/10 = 3/20
b) 4.(1/3 - x) + 1/2 = 5/6 +x
=> 4/3 - 4x + 1/2 = 5/6 +x
=> -4x - x = 5/6 - 4/3 - 1/2
=> -5x = -1
=> x= 1/5
c) 3. (1/2 - x) -5. ( x - 1/10) = -7/4
=> 3/2 - 3x - 5x + 1/2 = -7/4
=> -3x - 5x = -7/4 - 3/2 - 1/2
=> -8x = -15/4
=> x = 15/32
`@` `\text {Ans}`
`\downarrow`
Ta có: \(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\)
\(\Rightarrow\dfrac{3x-3}{6}=\dfrac{4y+12}{16}=\dfrac{5z-25}{30}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{3x-3}{6}=\dfrac{4y+12}{16}=\dfrac{5z-25}{30}\)`=`\(\dfrac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\)
`=`\(\dfrac{5z-25-3x+3-4y-12}{8}\)
`=`\(\dfrac{\left(5z-3x-4y\right)+\left(-25+3-12\right)}{8}\)
`=`\(\dfrac{50-34}{8}\)`=`\(\dfrac{16}{8}=2\)
`=>`\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=2\)
`=>`\(\left\{{}\begin{matrix}x=2\cdot2+1=5\\y=2\cdot4-3=5\\z=2\cdot6+5=17\end{matrix}\right.\)
Vậy, `x,y,z` lần lượt là `5; 5; 17.`
\(\frac{3}{4}\left(x-\frac{1}{2}\right)-\frac{5}{6}=\frac{1}{3}\)
\(\Leftrightarrow\frac{3}{4}x=\frac{3}{8}+\frac{5}{6}+\frac{1}{3}\)
\(\Leftrightarrow\frac{3}{4}x=\frac{37}{24}\)
\(\Leftrightarrow x=\frac{37}{18}\)
3/4.( x-1/2) = 1/3+ 5/6
3/4.(x- 1/2) = 7/6
x- 1/2 = 7/6: 3/4
x- 1/2 = 14/9
x = 14/9+ 1/2
x = 37/18