Bài 6:
a) \(x+5-\left(-11\right)=31-48\)
\(\Rightarrow x+5+11=-17\)
\(\Rightarrow x+16=-17\)
\(\Rightarrow x=-17-16\)
\(\Rightarrow x=-33\)
b) \(21+\left(-21+x\right)=252-\left(25+252\right)\)
\(\Rightarrow21-21+x=252-25-252\)
\(\Rightarrow0+x=\left(252-252\right)-25\)
\(\Rightarrow x=0-25\)
\(\Rightarrow x=-25\)
c) \(1^{2021}+99\left(5-x\right)=94-\left(-321\right)+279\)
\(\Rightarrow1+99\left(5-x\right)=94+321+279\)
\(\Rightarrow1+99\left(5-x\right)=600+94\)
\(\Rightarrow99\left(5-x\right)=694-1\)
\(\Rightarrow99\left(5-x\right)=693\)
\(\Rightarrow5-x=693:99\)
\(\Rightarrow5-x=7\)
\(\Rightarrow x=-2\)
d) \(x-\left(36-x\right)=-48-12+112\)
\(\Rightarrow x-36+x=-48+\left(-12+112\right)\)
\(\Rightarrow x\cdot\left(1+1\right)-36=-48+100\)
\(\Rightarrow2\cdot x-36=52\)
\(\Rightarrow2\cdot x=52+36\)
\(\Rightarrow2\cdot x=88\)
\(\Rightarrow x=88:2\)
\(\Rightarrow x=44\)
e) \(72:\left(x-2\right)^2=8\)
\(\Rightarrow\left(x-2\right)^2=72:8\)
\(\Rightarrow\left(x-2\right)^2=9\)
\(\Rightarrow\left(x-2\right)^2=3^2\)
\(\Rightarrow\left[{}\begin{matrix}x=2+3\\x=-3+2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
f) \(75-5\left(x-3\right)^3=700\)
\(\Rightarrow5\left(x-3\right)^3=75-700\)
\(\Rightarrow5\left(x-3\right)^3=-625\)
\(\Rightarrow\left(x-3\right)^3=-625:5\)
\(\Rightarrow\left(x-3\right)^3=-125\)
\(\Rightarrow\left(x-3\right)^3=\left(-5\right)^3\)
\(\Rightarrow x-3=-5\)
\(\Rightarrow x=-5+3\)
\(\Rightarrow x=-2\)
7:
a: 6 chia hết cho x+2
=>x+2 thuộc {1;-1;2;-2;3;-3;6;-6}
=>x thuộc {-1;-3;0;-4;1;-5;4;-8}
b: x+13 chia hết cho x+8
=>x+8+5 chia hết cho x+8
=>x+8 thuộc {1;-1;5;-5}
=>x thuộc {-7;-9;-3;-13}
c: 3x+2 chia hết cho x-3
=>3x-9+11 chia hết cho x-3
=>x-3 thuộc {1;-1;11;-11}
=>x thuộc {4;2;14;-8}
d: 3x+9 chia hết cho 2x+1
=>6x+18 chia hết cho 2x+1
=>6x+3+15 chia hết cho 2x+1
=>2x+1 thuộc {1;-1;3;-3;5;-5;15;-15}
=>x thuộc {0;-1;1;-2;2;-3;7;-8}
