tim x de
15-3x>x-7
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\(\left(x-1\right)\left(3x-7\right)=\left(x-1\right)\left(x+3\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-7\right)-\left(x+1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(\left(3x-7\right)-\left(x+3\right)\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(3x-7-x-3\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(2x-10\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\2x-10=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)
(x-1)(3X-7)=(x-1)(x+3)
=>(x-1)(3x-7)-(x-1)(x+3)=0
=>(x-1)(3x-7-x-3)=0
=>(x-1)(2x-10)=0
=> + x-1=0 =>x=1
+ 2x-10=0 =>x=5
a. \(\left(2x-3\right)\left(x+1\right)+\left(2x-3\right)\left(3x-7\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x+1+3x-7\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(4x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\4x-6=0\end{matrix}\right.\)\(\Leftrightarrow x=\dfrac{3}{2}\)
b. \(\left(x-4\right)\left(3x-2\right)+x^2-16=0\)
\(\Leftrightarrow\left(x-4\right)\left(3x-2\right)+\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(3x-2+x+4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(4x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\4x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{1}{2}\end{matrix}\right.\)
(2x-3)(x+1)+(2x+3)(3x-7)=0
<=> (2x-3)(x+1)-(2x-3)(3x-7)=0
<=> (2x-3)(x+1-3x+7)=0
<=> (2x-3)(-2x+8)=0
<=> 2x-3=0 => x=3/2
Hoặc -2x+8=0 => x= 4
Vậy x thuộc{3/2;4}
Xét x là số tự nhiên :
Ta có :
3x + 7 = 3x + 3 + 4 = 3.(x + 1) + 4 chia hết cho x + 1
<=> 4 chia hết cho x + 1
<=> x + 1 \(\in\) {1; 2; 4}
<=> x \(\in\) {0; 1; 3}
x e {5;4;3;2;1;0}