a)\(-\left(a-c\right)-\left(a-b+c\right)\)

\(=-a+c-a+b-c\)

\(=\left(-a-a\right)+\left(c-c\right)+b\)

\(=-2a+b=0\)

\(-2a=b\)

b)\(-\left(a-b+c\right)-\left(a+b+c\right)\)

\(=-a+b-c-a-b-c\)

\(=\left(-a-a\right)+\left(b-b\right)+\left(-c-c\right)\)

\(=-2a+0=-2c\)

\(=-2a+-2c\)

c)\(\left(a+b\right)-\left(a-b\right)+\left(a-c\right)-\left(a+c\right)\)

\(=a+b-a+b+a-c-a-c\)

\(=\left(a-a+a-a\right)+\left(b+b\right)+\left(-c-c\right)\)

\(=0+2b+\left(-2c\right)\)

\(=2b+\left(-2c\right)\)

d)\(\left(a+b-c\right)+\left(a-b+c\right)-\left(b+c-a\right)-\left(a-b-c\right)\)

\(=a+b-c+a-b+c-b-c+a-a+b+c\)

\(=\left(a+a+a-a\right)+\left(b-b-b+a\right)+\left(-c+c-c+c\right)\)

\(=2a+0+0\)

\(=2a\)

a)-(a-c)-(a-b+c)

=-a+c-a+b-c

=-2a+b

b)-(a-b+c)-(a+b+c)

=-a+b-c-a-b-c

=-2a-2c

=-2(a+c)

c)(a+b)-(a-b)+(a-c)-(a+c)

=a+b-a+b+a-c-a-c

=2b-2c

=2(b-c)

d)(a+b-c)+(a-b+c)-(b+c-a)-(a-b-c)

=a+b-c+a-b+c-b-c+a-a+b+c

=2a

a: \(\Leftrightarrow x-2\in\left\{1;-1;19;-19\right\}\)

hay \(x\in\left\{3;1;21;-17\right\}\)

b: \(\Leftrightarrow2x+3\in\left\{1;-1;3;-3\right\}\)(vì x là số nguyên nên 2x+3 là số lẻ)

hay \(x\in\left\{-1;-2;0;-3\right\}\)

c: \(\Leftrightarrow x+1+4⋮x+1\)

\(\Leftrightarrow x+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(x\in\left\{0;-2;1;-3;3;-5\right\}\)

d: \(\Leftrightarrow x+1⋮x+4\)

\(\Leftrightarrow x+4\in\left\{1;-1;3;-3\right\}\)

hay \(x\in\left\{-3;-5;-1;-7\right\}\)

a: \(\left(A\cap B\right)\cap C=(4;10]\cap\left(5;+\infty\right)=(5;10]\)

c: A\B=[3;4]

B\C=(4;5]

C\A=[3;5]

d: (A\B) giao C=[3;4] giao (5;+\(\infty\))=[4;5)

a/ \(\left\{{}\begin{matrix}-\frac{b}{2a}=2\\-\frac{b^2+4a}{4a}=3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}b=-4a\\b^2+16a=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=-1\\b=4\end{matrix}\right.\)

b/ \(\left\{{}\begin{matrix}-\frac{b}{2a}=1\\2=9a+3b-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=1\\b=-2\end{matrix}\right.\)

c/ \(\left\{{}\begin{matrix}a+b-1=2\\4a+2b-1=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=-2\\b=5\end{matrix}\right.\)