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a) \(\left(\frac{2x}{5}-1\right):\left(-5\right)=\frac{1}{7}\)
\(\frac{2x}{5}-1=\frac{1}{7}.\left(-5\right)\)
\(\frac{2x}{5}-1=\frac{-5}{7}\)
\(\frac{2x}{5}=\frac{-5}{7}+\frac{7}{7}\)
\(\frac{2x}{5}=\frac{2}{7}\)
\(=>2x.7=2.5\)
\(=>14x=10\)
\(=>x=\frac{5}{7}\)
c) \(\left|3,5+2,5x\right|-2,5=3,5\)
\(\left|3,5+2,5x\right|=3,5+2,5\)
\(\left|3,5+2,5x\right|=6\)
\(TH1\) \(3,5+2,5x=6\) \(TH2\) \(3,5+2,5x=-6\)
\(2,5x=6-3,5\) \(2,5x=-6-3,5\)
\(2,5x=2,5\) \(2,5x=-9.5\)
\(x=1\) \(x=-3,8\)
vậy \(x=1\) hoặc \(x=-3,8\)
câu d) làm tương tự như câu c)
Ta có :
\(\frac{x-1}{27}+\frac{x-2}{26}+\frac{x-3}{25}+\frac{x-4}{24}=4\)
\(\Leftrightarrow\)\(\left(\frac{x-1}{27}-1\right)+\left(\frac{x-2}{26}-1\right)+\left(\frac{x-3}{25}-1\right)+\left(\frac{x-4}{24}-1\right)=4-4\) ( trừ 2 vế cho 4 )
\(\Leftrightarrow\)\(\frac{x-28}{27}+\frac{x-28}{26}+\frac{x-28}{25}+\frac{x-28}{24}=0\)
\(\Leftrightarrow\)\(\left(x-28\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}\right)=0\)
Vì \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}\ne0\)
Nên \(x-28=0\)
\(\Rightarrow\)\(x=28\)
Vậy \(x=28\)
Chúc bạn học tốt ~
\(x-\frac{1}{27}+x-\frac{2}{26}+x-\frac{3}{25}+x-\frac{4}{24}=4\)
\(\left(x+x+x+x\right)-\left(\frac{1}{27}+\frac{2}{26}+\frac{3}{25}+\frac{4}{24}\right)=4\)
\(4x-\frac{7031}{17550}=4\)
\(4x=4+\frac{7031}{17550}\)
\(x=\frac{4+\frac{7031}{17550}}{4}=1+\frac{\frac{7031}{17550}}{4}\)
\(x=1+\frac{7031}{70200}\)
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Bài 1 d)
\(1-2+3-4+5-6+...+2013\)
\(=1+\left(-2+3\right)+\left(-4+5\right)+...+\left(-2012+2013\right)\)
\(=1+1+1+...+1\left(1006s\right)\)
\(=1006.1=1006\)
( 105 - X ) : 25 = 1+ 1
( 105 - X ) : 25 = 2
( 105 - X ) = 50
X = 105 - 50
X = 55
\(\left(2-x\right)^3=\left(2-x\right)^5\)
\(\Leftrightarrow\left(2-x\right)^5-\left(2-x\right)^3=0\)
\(\Leftrightarrow\left(2-x\right)^3\left[\left(2-x\right)^2-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2-x\right)^3=0\\\left(2-x\right)^2=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2-x=0\\2-x=1\\2-x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=1\\x=3\end{matrix}\right.\)
(2 - \(x\))3 = (2 - \(x\))5
(2 - \(x\))3 - (2 - \(x\))5 = 0
(2 - \(x\))3.[1 - (2 - \(x\))2] = 0
\(\left[{}\begin{matrix}\left(2-x\right)^3=0\\1-\left(2-x\right)^2=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}2-x=0\\\left(2-x\right)^2=1\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=2\\2-x=-1\\2-x=1\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)
Vậy \(x\) \(\in\) {1; 2; 3}
25x+2:5x+1=1254
52x+4:5x+2=512
52x+4-x-2=512
5x+2=512
=> x+2=12
x=12-2
x=10
Vậy x=10
tk nha!
\(25^{x+2}:5^{x+1}=125^4\)
\(\Leftrightarrow\left(5^2\right)^{\left(x+2\right)}:5^{x+1}=\left(5^3\right)^4\)\(\Leftrightarrow5^{2x+4}:5^{x+1}=5^{12}\)
\(\Leftrightarrow5^{\left(2x+4\right)-\left(x+1\right)}=5^{12}\Leftrightarrow\left(2x+4\right)-\left(x+1\right)=12\)
\(\Leftrightarrow2x+4-x-1=12\Leftrightarrow3=12\) ( vô lý )
Vậy không có giá trị của x là số tự nhiên thỏa mãn đề bài
Lời giải:
$x-25\text{%}x-\frac{1}{2}=\frac{-5}{4}$
$x-0,25x=\frac{1}{2}-\frac{5}{4}$
$x(1-0,25)=\frac{-3}{4}$
$x.0,75=\frac{-3}{4}$
$x=\frac{-3}{4}: 0,75=\frac{-3}{4}: \frac{3}{4}=-1$
x - 25% .x - 1/2 = -5/4
x - 1/4 . x - 1/2 = -5/4
(x.x ) - (1/4 - 1/2) = -5/4
2x - -1/4 = -5/4
2x + 1/4 = -5/4
2x = -5/4 - 1/4
2x = -3/2
x = -3/2 : 2 ( -3/2 x 1/2)
x = -3/4