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a,3/4 . (-5/12)+3/4.(-7/12)
` 3/4 . [ - ( 5/12 + 7/12 ) ] `
`3/4 . (-1) = -3/4 `
`2/3 . x - 0,5 = 3/4 `
` x - 0,5 = 3/4 - 2/3 `
` x-0,5 = 1/12 `
` x = 1/12 + 0,5 `
` x= 7/12 `
Bài 2:
a: =>2/3x=3/4+1/2=3/4+2/4=5/4
=>x=5/4:2/3=5/4*3/2=15/8
b:=>-2x+4=3x-12
=>-5x=-16
=>x=16/5
\(\dfrac{x+3}{12}=\dfrac{3}{x+3}\)(ĐKXĐ: x<>-3)
=>\(\left(x+3\right)^2=3\cdot12=36\)
=>\(\left[{}\begin{matrix}x+3=6\\x+3=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-9\end{matrix}\right.\)
\(\dfrac{x+3}{12}=\dfrac{3}{x+3}\) (đk: \(x\neq-3\))
\(\Rightarrow\left(x+3\right)\cdot\left(x+3\right)=3\cdot12\)
\(\Rightarrow\left(x+3\right)^2=36\)
\(\Rightarrow\left(x+3\right)^2=\left(\pm6\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x+3=6\\x+3=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-9\left(tm\right)\end{matrix}\right.\)
Vậy \(x\in\left\{3;-9\right\}\).
\(\dfrac{x+3}{12}=\dfrac{3}{x+3}\\ \Rightarrow\left(x+3\right)\left(x+3\right)=12.3\\ \Rightarrow x^2+6x+9=36\\ \Rightarrow x^2+6x+9-36=0\\ \Rightarrow x^2+6x-27=0\\ \Rightarrow x^2-3x+9x-27=0\\ \Rightarrow x\left(x-3\right)+9\left(x-3\right)=0\\ \Rightarrow\left(x+9\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-3=0\\x+9=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-9\end{matrix}\right.\)
Trả lời :
a, \(\frac{3}{4}-\left(\frac{1}{2}\div x+\frac{1}{2}\right)=\frac{3}{5}\)
=> \(\frac{1}{2}\div x+\frac{1}{2}=\frac{3}{20}\)
=> \(\frac{1}{2}\div x=\frac{-7}{20}\)
=> \(x=\frac{-10}{7}\)
b, (4 - x) . (2x + 3) = 0
=> \(\orbr{\begin{cases}4-x=0\\2x+3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=4\\x=\frac{-3}{2}\end{cases}}\)
c, \(\frac{4}{-3}=\frac{-12}{x}\)
=> 4x = 36
=> x = 9
d, \(\frac{4x}{-3}=\frac{12}{-x}\)
=> \(-4x^2=-36\)
=> 4x2 = 36
=> x2 = 9
=> x = \(\pm3\)
\(\dfrac{-4}{x}=\dfrac{x}{-49}\\ \Rightarrow x^2=\left(-4\right)\left(-49\right)\\ \Rightarrow x^2=196\\ \Rightarrow x=\pm14\)
\(\dfrac{3.6}{x-3}=\dfrac{5}{3}\\ \Rightarrow5\left(x-3\right)=3.3.6\\ \Rightarrow5\left(x-3\right)=54\\ \Rightarrow x-3=\dfrac{54}{5}\\ \Rightarrow x=\dfrac{54}{5}+3\\ \Rightarrow x=\dfrac{69}{15}\)
\(\left(2x+1\right):2=12:3\\ \left(2x+1\right):2=4\\2x+1=2\\ 2x=1\\ x=\dfrac{1}{2} \)
\(\left(2x-14\right):3=12:9\\ \left(2x-14\right):3=\dfrac{4}{3}\\ 2x-14=4\\ 2x=16\\ x=8\)
3 | x + 3 | + | 3x - 3 | = 12 ( 1 )
Xét x + 3 = 0 => x = -3
3x - 3 = 0 => x = 1
Lập bảng xét dấu :
x - 3 1
x + 3 - 0 + | +
3x - 3 - | - 0 +
Với x \(\le\) -3 thì từ ( 1 ) => 3 . ( -3 - x ) + ( 3 - 3x ) = 12
-9 - 3x + 3 - 3x = 12
-6 - 6x = 12
6x = -18
x = -3 ( thỏa mãn )
với -3 < x \(\le\)1 thì từ ( 1 ) => 3 . ( x + 3 ) + ( 3 - 3x ) = 12
3x + 9 + 3 - 3x = 12
0x = 12 ( không thỏa mãn )
Với x > 1 thì từ ( 1 ) => 3 . ( x + 3 ) + ( 3x - 3 ) = 12
3x + 9 + 3x - 3 = 12
6x - 6 = 12
6x = 18
x = 3 ( thỏa mãn )
Vậy x = { -3 ; 3 }
Bạn ghi đề bằng latex cho dễ hiểu nhé.
\(x-\frac{3}{12}=\frac{-3}{3}-x\)
\(\Rightarrow x+x=\frac{-3}{3}+\frac{3}{12}\)
\(\Rightarrow2x=\frac{-3}{4}\)
\(\Rightarrow x=\frac{-3}{4}:2\)
\(\Rightarrow x=\frac{-3}{8}\)