Tìm x :
\(2.|5x-3|-x=7\)
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a)
<=> 10x - 35 + 16x - 10 = 5
<=> 10x + 16x = 5 + 35 + 10
<=> 26x = 50
<=> x = 50/26 = 25/13
ta có
a. (5x-7)(x-9)-(-x+3)(-5x+2)= 2x(x-4)-(x-1)(2x+3)
\(\Leftrightarrow5x^2-52x+63-\left(5x^2-17x+6\right)=2x^2-8x-\left(2x^2+x-3\right)\)
\(\Leftrightarrow-35x+57=-9x+3\Leftrightarrow26x=54\Leftrightarrow x=\frac{27}{13}\)
b. (x-3)(-x+10)+(x-8)(x+3)= (5x^2-1)(x+3)-5x^3-15x^2
\(\Leftrightarrow-x^2+13x-30+x^2-5x-24=5x^3+15x^2-x-3-5x^3-15x^2\)
\(\Leftrightarrow8x-54=-x-3\Leftrightarrow9x=51\Leftrightarrow x=\frac{17}{3}\)
a) \(2.\left|5x-3\right|-2x=14\)
\(2\left|5x-3\right|=14+2x\)
\(\left|5x-3\right|=\frac{14+2x}{2}\)
\(\Rightarrow\orbr{\begin{cases}5x-3=\frac{-14-2x}{2}\\5x-3=\frac{14+2x}{2}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}\left(5x-3\right).2=-14-2x\\\left(5x-3\right).2=14+2x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}10x-6+2x=-14\\10x-6-2x=14\end{cases}\Rightarrow\orbr{\begin{cases}12x=-14+6\\8x=14+6\end{cases}}}\Rightarrow\orbr{\begin{cases}12x=-8\\8x=20\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-2}{3}\\x=2,5\end{cases}}\)
vậy \(\orbr{\begin{cases}x=\frac{-2}{3}\\x=2,5\end{cases}}\)
Những câu sau tương tự nhé.
a) \(\left(x-4\right)^2-\left(x-4\right)=0\)
\(\left(x-4\right)\left(x-4-1\right)=0\)
\(\left[{}\begin{matrix}x-4=0\\x-5=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
b) \(5x^2\left(x-7\right)+7\left(x-7\right)=0\)
\(\left(x-7\right)\left(5x^2+7\right)=0\)
\(\left[{}\begin{matrix}x-7=0\\5x^2+7=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=7\\x^2=\dfrac{-7}{5}\end{matrix}\right.\)
\(x=7\)
c) \(x^2\left(x-3\right)-\left(x-3\right)=0\)
\(\left(x-3\right)\left(x^2-1\right)=0\)
\(\left[{}\begin{matrix}x=3\\x=\pm1\end{matrix}\right.\)
a) (x - 4)^2=(x - 4)
(x - 4) (x -4)=(x -4 )
(x - 4) (x - 4)-(x - 4)=0
(x-4) (x-4-1)=0
(x-4) (x-5)=0
TH1:x-4=0 TH2:x-5=0
x=4 x=5
a) ( 5x + 1 )2 - ( 5x + 3 )( 5x - 3 ) = 30
⇔ 25x2 + 10x + 1 - ( 25x2 - 9 ) = 30
⇔ 25x2 + 10x + 1 - 25x2 + 9 = 30
⇔ 10x + 10 = 30
⇔ 10x = 20
⇔ x = 2
b) ( x + 3 )2 + ( x - 2 )( x + 2 ) - 2( x - 1 )2 = 7
⇔ x2 + 6x + 9 + x2 - 4 - 2( x2 - 2x + 1 ) = 7
⇔ 2x2 + 6x + 5 - 2x2 + 4x - 2 = 7
⇔ 10x + 3 = 7
⇔ 10x = 4
⇔ x = 4/10 = 2/5
1) 5x + 3 = 2(x + 7)
5x + 3 = 2x + 2.7
5x + 3 = 2x + 14
5x - 2x = 14 - 3
3x = 11
x = 11/3
Vậy x = 11/3
2) 5x - 25 = 2x - 3
5x - 2x = -3 + 25
3x = 22
x = 22/3
Vậy x = 22/3
\(2.|5x-3|-x=\)\(7\)
\(\Leftrightarrow\) \(2.|5x-3|=7+x\)
\(\Leftrightarrow\) \(|5x-3|=\frac{7+x}{2}\)
\(\Leftrightarrow\)\(5x-3=\pm\left(\frac{7+x}{2}\right)\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}5x-3=\frac{7+x}{2}\\5x-3=\frac{-7-x}{2}\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{2.\left(5x-3\right)}{2}=\frac{7+x}{2}\\\frac{2.\left(5x-3\right)}{2}=\frac{-7-x}{2}\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{10x-6}{2}=\frac{7+x}{2}\\\frac{10x-6}{2}=\frac{-7-x}{2}\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}10x-6=7+x\\10x-6=-7-x\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}10x-x=7+6\\10x+x=-7+6\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}9x=13\\11x=-1\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{13}{9}\\x=\frac{-1}{11}\end{cases}}\)
Vậy x = \(\frac{13}{9}\) , x = \(\frac{-1}{11}\)