\(a,x^2-\dfrac{4}{3}x=0\)
\(\Leftrightarrow x\left(x-\dfrac{4}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)
\(b,\left|3x+7\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+7=5\\3x+7=-5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}3x=-2\\3x=-12\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=-4\end{matrix}\right.\)
\(c,2\left|7-2x\right|=6\)
\(\Leftrightarrow\left|7-2x\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}7-2x=3\\7-2x=-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=10\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)
\(d,5\left(x+2\right)+2\left(x-1\right)=10\)
\(\Leftrightarrow5x+10+2x-2=10\)
\(\Leftrightarrow7x+8=10\)
\(\Leftrightarrow7x=2\Leftrightarrow x=\dfrac{2}{7}\)
\(e,6\left(x-3\right)-4\left(x+2\right)=15\)
\(\Leftrightarrow6x-18-4x-8=15\)
\(\Leftrightarrow2x-26=15\)
\(\Leftrightarrow2x=41\Leftrightarrow x=\dfrac{41}{2}\)
\(g,\left(12-2x\right)^2=\dfrac{4}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}12-2x=\dfrac{2}{3}\\12-2x=-\dfrac{2}{3}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{34}{3}\\2x=\dfrac{38}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{17}{3}\\x=\dfrac{19}{3}\end{matrix}\right.\)
a) x² - 4/3 x = 0
x(x - 4/3) = 0
x = 0 hoặc x - 4/3 = 0
*) x - 4/3 = 0
x = 4/3
Vậy x = 0; x = 4/3
b) |3x + 7| = 5
3x + 7 = 5 và 3x + 7 = -5
*) 3x + 7 = 5
3x = 5 - 7
3x = -2
x = -2/3
*) 3x + 7 = -5
3x = -5 - 7
3x = -12
x = -12 : 3
x = -4
Vậy x = -4; x = -2/3
c) 2|7 - 2x| = 6
|7 - 2x| = 6 : 2
|7 - 2x| = 3
7 - 2x = 3 và 7 - 2x = -3
*) 7 - 2x = 3
2x = 7 - 3
2x = 4
x = 4 : 2
x = 2
*) 7 - 2x = -3
2x = 7 + 3
2x = 10
x = 10 : 2
x = 5
Vậy x = 2; x = 5
d) 5(x + 2) + 2(x - 1) = 10
5x + 10 + 2x - 2 = 10
7x + 8 = 10
7x = 10 - 8
7x = 2
x = 2/7
e) 6(x - 3) - 4(x + 2) = 15
6x - 18 - 4x - 8 = 15
2x - 26 = 15
2x = 15 + 26
2x = 41
x = 41/2
g) (12 - 2x)² = 4/9
12 - 2x = 2/3 hoặc 12 - 2x = -2/3
*) 12 - 2x = 2/3
2x = 12 - 2/3
2x = 34/3
x = 34/3 : 2
x = 17/3
*) 12 - 2x = -2/3
2x = 12 + 2/3
2x = 38/3
x = 38/3 : 2
x = 19/3
Vậy x = 17/3; x = 19/3
a) \(x^2-\dfrac{4}{3}x=0\)
\(\Rightarrow x\left(x-\dfrac{4}{3}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{4}{3}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)
b) \(\left|3x+7\right|=5\)
\(\Rightarrow\left[{}\begin{matrix}3x+7=5\left(ĐK:x\ge-\dfrac{7}{3}\right)\\3x+7=-5\left(ĐK:x< -\dfrac{7}{3}\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=-2\\3x=-12\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\left(tm\right)\\x=-4\left(tm\right)\end{matrix}\right.\)
c) \(2\left|7-2x\right|=6\)
\(\Rightarrow\left[{}\begin{matrix}2\left(7-2x\right)=6\left(ĐK:x\le\dfrac{7}{2}\right)\\2\left(7-2x\right)=-6\left(ĐK:x>\dfrac{7}{2}\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}14-4x=6\\14-4x=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-4x=-8\\-4x=-20\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=5\left(tm\right)\end{matrix}\right.\)
d) \(5\left(x+2\right)+2\left(x-1\right)=10\)
\(\Rightarrow5x+10+2x-2=10\)
\(\Rightarrow7x+8=10\)
\(\Rightarrow7x=10-8\)
\(\Rightarrow7x=2\)
\(\Rightarrow x=\dfrac{2}{7}\)
e) \(6\left(x-3\right)-4\left(x+2\right)=15\)
\(\Rightarrow6x-18-4x-8=15\)
\(\Rightarrow2x-26=15\)
\(\Rightarrow2x=15+26\)
\(\Rightarrow2x=41\)
\(\Rightarrow x=\dfrac{41}{2}\)
g) \(\left(12-2x\right)^2=\dfrac{4}{9}\)
\(\Rightarrow\left(12-2x\right)^2=\left(\dfrac{2}{3}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}12-2x=\dfrac{2}{3}\\12-2x=-\dfrac{2}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{34}{3}\\2x=\dfrac{38}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{17}{3}\\x=\dfrac{19}{3}\end{matrix}\right.\)
