Question

1,a. 12(x-5)+7(3-x)=15

b,30(x+2)-6(x-5)-24x=100

2a, (x-3)(2y+1)=7

b,(2x+1)(3y-2)=-55

c,xy+3x-7y=21

d,xy-x+3y=13

Answer 1

1)

a/ \(12\left(x-5\right)+7\left(3-x\right)=15\)

\(\Rightarrow12x-12.5+7.3-7x=15\)

\(\Rightarrow12x-60+21-7x=15\)

\(\Rightarrow12x-7x=15+60-21\)

\(\Rightarrow5x=54\)

\(\Rightarrow x=\frac{54}{5}=10,8\)

b/ \(30\left(x+2\right)-6\left(x-5\right)-24x=100\)

\(\Rightarrow30x+30.2-6x-6.5-24x=100\)

\(\Rightarrow30x+60-6x+30-24x=100\)

\(\Rightarrow30x-6x-24x=100-60-30\)

\(\Rightarrow0x=10\)

\(\Rightarrow\) k có giá trị \(x\) nào thỏa mãn đề bài

Answer 2

\(12\left(x-5\right)+7\left(3-x\right)=15\)

\(12x-60+21-7x=15\)

\(12x-\left(60-21+7x\right)=15\)

\(12x-\left(39+7x=15\right)\)

\(12x-39-7x=15\)

\(5x=15+39\)

\(5x=54\)

\(x=10,8\)

Answer 3

vì \( (x-3)(2y+1)=7\) nên x-3 và 2y+1 là 2 số nguyên cùng dấu nhau

\(\Rightarrow\left\{\begin{matrix}x-3>0\\2y+1>0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x>3\\2y>1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x\in\left\{4,5,6,7,...\right\}\\y\in\left\{1,2,3,4,...\right\}\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}x-3< 0\\2y+1< 0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x< 3\\2y< 1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x\in\left\{2,1,0,...\right\}\\y\in\left\{0,-1,...\right\}\end{matrix}\right.\)

Answer 4

2)

a/ \(\left(x-3\right)\left(2y+1\right)=7\)

\(\Rightarrow\left(x-3\right);\left(2y+1\right)\inƯ_7\)

Ta có các trường hợp sau:

TH1: \(\left\{\begin{matrix}x-3=1\\2y+1=7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=4\\y=3\end{matrix}\right.\)

TH2: \(\left\{\begin{matrix}x-3=-1\\2y+1=-7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2\\y=-4\end{matrix}\right.\)

TH3: \(\left\{\begin{matrix}x-3=7\\2y+1=1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=10\\y=0\end{matrix}\right.\)

TH4: \(\left\{\begin{matrix}x-3=-7\\2y+1=-1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=-4\\y=-1\end{matrix}\right.\)

b/ tương tự a

c/ \(xy+3x-7y=21\)

\(\Rightarrow x\left(y+3\right)-7y-21=0\)

\(\Rightarrow x\left(y+3\right)-7\left(y+3\right)=0\)

\(\Rightarrow\left(y+3\right)\left(x-7\right)=0\)

\(\Rightarrow\left\{\begin{matrix}x-7=0\\y+3=0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=7\\y=-3\end{matrix}\right.\)

Vậy...........................

d/ tương tự c