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a: =>10|x-2|=50
=>|x-2|=5
=>x-2=5 hoặc x-2=-5
=>x=7 hoặc x=-3
b: =>|3x-12|+|5x-20|=56
=>8|x-4|=56
=>|x-4|=7
=>x-4=7 hoặc x-4=-7
=>x=11 hoặc x=-3
a) \(\left\{{}\begin{matrix}3x=4y\\x+y=-56\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}3x-4y=0\\x+y=-56\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}3x-4y=0\\4x+4y=-224\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}7x=-224\\x+y=-56\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=\dfrac{-224}{7}=-32\\x+y=-56\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=-32\\-32+y=-56\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=-32\\y=-24\end{matrix}\right.\) vậy \(x=-32;y=-24\)
b/ Theo đề ta có: \(\dfrac{x}{4}=\dfrac{x}{5}\Rightarrow\dfrac{x}{12}=\dfrac{x}{15}\)
\(\dfrac{x}{3}=\dfrac{y}{2}\Rightarrow\dfrac{x}{12}=\dfrac{y}{8}\)
\(\Rightarrow\dfrac{x}{12}=\dfrac{y}{8}=\dfrac{z}{15}\) và \(x+y-z=10\)
Áp dụng t/c của dãy tỉ số = nhau ta có:
\(\dfrac{x}{12}=\dfrac{y}{8}=\dfrac{z}{15}=\dfrac{x+y-z}{12+8-15}=\dfrac{10}{5}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\cdot12=24\\y=2\cdot8=16\\z=2\cdot15=30\end{matrix}\right.\)
Vậy.............
(-75) : (x + 6) = -15
x + 6 = -75 : (-15)
x + 6 = 5
x = 5 - 6
x = -1
B) -25 - 5.(x + 2) = 50
5(x + 2) = -25 - 50
5(x + 2) = -75
x + 2 = -75 : 5
x + 2 = - 15
x = -15 - 2
x = -17
D) 6.(2x - 8) - 8.(3x - 5) = -56
12x - 24 - 24x + 40 = -56
-12x + 16 = -56
-12x = -56 - 16
-12x = -72
x = (-72) : (-12)
x = 6
Lời giải:
a.
$-75:(x+6)=-15$
$x+6=(-75):(-15)=5$
$x=5-6=-1$
b.
$-25-5(x+2)=50$
$5(x+2)=-25-50=-75$
$x+2=-75:5=-15$
$x=-15-2=-17$
d.
$6(2x-8)-8(3x-5)=-56$
$(12x-48)-(24x-40)=-56$
$-12x-8=-56$
$-12x=-56+8=-48$
$x=(-48):(-12)=4$
x + 5 = 56
x = 56 - 5
x = 51
x = 51 . Vậy y bằng :
51 x 3 : 4 = 38 , 25
x = 51 y = 38 , 25
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8.2^3x.7^y=56^2x.5^x-1
=>8.8^x.7^y=(8.7)^2x.5^x-1
=>8^1+x.7^y=8^2x.7^2x.5^x-1
=>8^1+x.7^y / 8^2x.7^2x=5^x-1
=>8^x+1-2x . 7^y-2x = 5^x-1
=>8^1-x.7^y-2x=5^-(1-x)
=>8^1-x.7^y-2x=1/5^1-x
=>8^1-x.7^y-2x.5^1-x=1
=>(8.5)^x-1.7^y-2x=1
=>40^x-1.7^y-2x=1
=>x-1=0 và y-2x=0
=>x=1 và y=2
a) \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7};x+y+z=56\)
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{56}{14}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=4.2=8\\y=4.5=20\\z=4.7=28\end{matrix}\right.\)
b) \(\dfrac{x}{1,1}=\dfrac{y}{1,3}=\dfrac{z}{1,4}\left(1\right);2x-y=5,5\)
\(\left(1\right)\Rightarrow\dfrac{2x-y}{1,1.2-1,3}=\dfrac{5,5}{0,9}\)
\(\Rightarrow\left\{{}\begin{matrix}x=1,1.\dfrac{5,5}{0,9}=\dfrac{6,05}{0,9}\\y=1,3.\dfrac{5,5}{0,9}=\dfrac{7,15}{0,9}\\z=\dfrac{1,4}{1,1}.x=\dfrac{1,4}{1,1}.\dfrac{6,05}{0,9}=\dfrac{8,47}{0,99}\end{matrix}\right.\)
d) \(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5};xyz=-30\)
\(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5}=\dfrac{xyz}{2.3.5}=\dfrac{-30}{30}=-1\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-1\right)=-2\\y=3.\left(-1\right)=-3\\z=5.\left(-1\right)=-5\end{matrix}\right.\)
x - 56/5 = -3x + 4
x + 3x = 4 + 56/5
4x = 76/5
x = 76/5 : 4
x = 19/5
`@` `\text {Ans}`
`\downarrow`
\(x-\dfrac{56}{5}=-3x+4\)
`\Rightarrow `\(x-\dfrac{56}{5}+3x-4=0\)
`\Rightarrow `\(\left(x+3x\right)+\left(-\dfrac{56}{5}-4\right)=0\)
`\Rightarrow `\(4x-\dfrac{76}{5}=0\)
`\Rightarrow `\(4x=\dfrac{76}{5}\)
`\Rightarrow `\(x=\dfrac{76}{5}\div4\)
`\Rightarrow `\(x=\dfrac{19}{5}\)
Vậy, `x=`\(\dfrac{19}{5}\)