4:

(x+1)(y-2)=5

=>\(\left(x+1;y-2\right)\in\left\{\left(1;5\right);\left(5;1\right);\left(-1;-5\right);\left(-5;-1\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(0;7\right);\left(4;3\right);\left(-2;-3\right);\left(-6;1\right)\right\}\)

Answer:

a. \(-5< x< 5\)

\(\Rightarrow x\in\left\{\pm4;\pm3;\pm2;\pm1;0\right\}\)

Tổng các số nguyên x thoả mãn:

\((-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4\)

\(= (4 - 4) + (3 - 3) + (2 - 2) + (1 - 1) + 0\)

\(=0\)

a, \(x\in\left\{-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)

Tổng các x thoả mãn: (-5+5)+(-4+4)+(-3+3)+(-2+2)+(-1+1)+0=0+0+0+0+0+0=0

b, \(x\in\left\{-3;-2;-1;0;1;2\right\}\)

Tổng các x thoả mãn: (-2+2) + (-1+1) + 0 + (-3) = 0 + 0 + 0 + (-3) = -3

c, \(x\in\left\{-1;0;1;2;3;4\right\}\)

Tổng các x thoả mãn: (-1+1) + 0 + 2 + 3 + 4 = 9

Tương tự cháu làm các câu d,e,f rồi gửi lên lại thầy check cho hí

\(\text{a) -5 ≤ x < 6 }\)

\(x\in\left\{-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)

\(\text{b) -4 < x < 3}\)

\(x\in\left\{-3;-2;-1;0;1;2\right\}\)
\(\text{c) -1 ≤ x ≤ 4}\)

\(x\in\left\{-1;0;1;2;3;4\right\}\)               

\(\text{d) -5 < x < 2}\)

\(x\in\left\{-4;-3;-2;-1;0;1\right\}\)
\(\text{e) -5 < x < 5 }\)

\(x\in\left\{-4;-3;-2;-1;0;1;2;3;4\right\}\)

\(\text{f) -6 < x ≤ 4}\)

\(x\in\left\{-5;-4;-3;-2;-1;0;1;2;3;4\right\}\)

`Answer:`

`1/5+2/7-1<x<\frac{13}{3}+6/5+\frac{4}{15}`

`VT =1/5+2/7-1=\frac{17}{35}-1=\frac{-18}{35}`

`VP=\frac{13}{3}+6/5+\frac{4}{15}=\frac{83}{15}+\frac{4}{15}=\frac{203}{35}`

`=>\frac{-18}{35}<x<\frac{203}{35}`

`=>-18<x<203`

Vậy `-18<x<203` với `x\inZZ`

\(\dfrac{1}{5}+\dfrac{2}{7}-1< x< \dfrac{13}{3}+\dfrac{6}{5}+\dfrac{4}{15}\)

\(\Leftrightarrow\dfrac{7}{35}+\dfrac{10}{35}-\dfrac{35}{35}< x< \dfrac{65}{15}+\dfrac{18}{15}+\dfrac{4}{15}\)

\(\Leftrightarrow\dfrac{-18}{35}< x< \dfrac{29}{5}\)

\(\Leftrightarrow\dfrac{-18}{35}< \dfrac{35x}{35}< \dfrac{203}{35}\)

\(\Leftrightarrow-18< 35x< 203\)

\(\Leftrightarrow x\in\left\{0;1;2;3;4;5\right\}\)

Bài 4:

\(\left|x+1\right|+\left|2x-3\right|=x-2\)

\(\Leftrightarrow x-2=\left|x+1\right|+\left|2x-3\right|\ge0\)

\(\Leftrightarrow x\ge2\)

\(\Leftrightarrow x+1>0\Leftrightarrow\left|x+1\right|=x+1\)

\(\Leftrightarrow2x-3>0\Leftrightarrow\left|2x-3\right|=2x-3\)

Lúc đó:

\(x+1+2x-3=x-2\)

\(\Leftrightarrow3x-2=x-2\Leftrightarrow x=0\)(Vô lý)

Bài 5:

\(\left|x-1\right|+\left|x-2\right|+\left|x-3\right|=5\)

Trường hợp 1: \(x\ge3\)

\(\left|x-1\right|=x-1\)

\(\left|x-2\right|=x-2\)

\(\left|x-3\right|=x-3\)

Lúc đó:

\(x-1+x-2+x-3=5\)

\(\Leftrightarrow3x-6=5\Leftrightarrow x=\frac{11}{3}\)(Thỏa mãn)

Trường hợp 2: \(2\le x\le3\)

\(\left|x-1\right|=x-1\)

\(\left|x-2\right|=x-2\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(x-1+x-2+3-x=5\)

\(\Leftrightarrow2x=5\Leftrightarrow x=\frac{5}{2}\)(Thỏa mãn)

Trường hợp 3:\(1\le x\le2\)

\(\left|x-1\right|x=x-1\)

\(\left|x-2\right|=2-x\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(x-1+2-x+3-x=5\)

\(\Leftrightarrow4-x=5\Leftrightarrow x=\left(-1\right)\)(Loại)

Trường hợp 4: \(x< 1\)

\(\left|x-1\right|=1-x\)

\(\left|x-2\right|=2-x\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(1-x+2-x+3-x=5\)

\(\Leftrightarrow6-3x=5\Leftrightarrow x=\frac{1}{3}\)(Thỏa mãn)