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a.
\(10⋮\left(x-1\right)\)
\(\Rightarrow x-1=Ư\left(10\right)\)
\(\Rightarrow x-1=\left\{-10;-5;-2;-1;1;2;5;10\right\}\)
\(\Rightarrow x=\left\{-9;-4;-1;0;2;3;6;11\right\}\)
b.
\(\left(x+5\right)⋮\left(x-2\right)\Rightarrow\left(x-2\right)+7⋮x-2\)
\(\Rightarrow7⋮x-2\)
\(\Rightarrow x-2=Ư\left(7\right)=\left\{-7;-1;1;7\right\}\)
\(\Rightarrow x=\left\{-5;1;3;9\right\}\)
c.
\(\left(3x+8\right)⋮\left(x-1\right)\)
\(\Rightarrow\left(3x-3+11\right)⋮\left(x-1\right)\)
\(\Rightarrow3\left(x-1\right)+11⋮x-1\)
\(\Rightarrow11⋮\left(x-1\right)\)
\(\Rightarrow x-1=Ư\left(11\right)=\left\{-11;-1;1;11\right\}\)
\(\Rightarrow x=\left\{-10;0;2;12\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(-2\left(x+6\right)=8-6\left(x-10\right)\)
\(\Leftrightarrow-2x-12=8-6x+60\)
\(\Leftrightarrow-2x-12=-6x+68\)
\(\Leftrightarrow-2x=-6x+68+12\)
\(\Leftrightarrow-2x=-6x+80\)
\(\Leftrightarrow-2x+6x=80\)
\(\Leftrightarrow4x=80\)
\(\Leftrightarrow x=20\)
Vậy \(x=20\)
b) \(-4\left(2x+9\right)=\left(x+13\right)+\left(-8x+3\right)\)
\(\Leftrightarrow-4\left(2x+9\right)=x+13+-8x+3\)
\(\Leftrightarrow-4\left(2x+9\right)=x+13-8x+3\)
\(\Leftrightarrow-4\left(2x+9\right)=-7x+16\)
\(\Leftrightarrow-8x-36=-7x+16\)
\(\Leftrightarrow-36=-7x+16+8x\)
\(\Leftrightarrow x+16=-36\)
\(\Leftrightarrow x=-52\)
Vậy \(x=-52\)
a) -2(x+6)=8-6(x-10)
<=> -2x-12=8-6x+60
<=> -2x-12-68+6x=0
<=> 4x-80=0
<=> 4x=80
<=> x=20
b) -4(2x+9)=(x+13)+(-8x+3)
<=> -8x-36=x+13-8x+3
<=> -8x-36=-7x+16
<=> -8x-36+7x-16=0
<=> -x-52=0
<=> -x=52
<=> x=-52
![](https://rs.olm.vn/images/avt/0.png?1311)
Lí luận chung cho cả 4 câu :
Để tích này bé hơn 0 thì các thừa số phải trái dấu với nhau
a) Dễ thấy \(x-2>x-7\)
\(\Rightarrow\hept{\begin{cases}x-2>0\\x-7< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x>2\\x< 7\end{cases}\Leftrightarrow}2< x< 7}\)
b) tương tự
c) \(\left(x^2-1\right)\left(x^2-4\right)\left(x^2-7\right)\left(x^2-10\right)< 0\)
\(\Leftrightarrow\left(x^4-11x^2+10\right)\left(x^4-11x^2+28\right)< 0\)
Dễ thấy \(x^4-11x^2+10< x^4-11x^2+28\)
\(\Rightarrow\hept{\begin{cases}x^4-11x^2+10< 0\\x^4+11x^2+10>0\end{cases}}\)
Tự giải nốt nha bạn mình bận rồi
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow-\dfrac{3}{4}< =x< =\dfrac{1}{2}\)
hay x=0
![](https://rs.olm.vn/images/avt/0.png?1311)
Tìm x, biết:
3(x+2)(x+5) +5(x+5)(x+10) +7(x+10)(x+17) =x(x+2)(x+17) (x∉−2;−5;−10;−17)
2(x−1)(x−3) +5(x−3)(x−8) +12(x−8)(x−20) −1x−20 =−34 (x∉1;3;8;20)
x+110 +2+111 x+112 =x+113 +x+114
x−1030 +x−1443 +x−595 +x−1488 =0
x không thể nào =2 được
chắc là x thuộc \(\phi\)