Bài 5: Cộng hai số nguyên khác dấu

a) Ta có: \(4\left(x-2\right)-2\left(x+3\right)=-28\)

\(\Leftrightarrow4x-8-2x-6+28=0\)

\(\Leftrightarrow2x+14=0\)

\(\Leftrightarrow2x=-14\)

hay x=-7

Vậy: x=-7

b) Ta có: \(3x+7-9x=-11\)

\(\Leftrightarrow-6x+7+11=0\)

\(\Leftrightarrow-6x+18=0\)

\(\Leftrightarrow-6x=-18\)

hay x=3

Vậy: x=3

a) 

\(\left(x+1\right)\left(y-2\right)=5\\ \Rightarrow\left(x+1\right),\left(y-2\right)\inƯ\left(5\right)=\left\{1;-1;5;-5\right\}\)

Ta có bảng:

Vậy \(\left(x;y\right)=\left(0;7\right),\left(-2;-3\right),\left(4;3\right),\left(-6;1\right)\)

b) 

\(\left(x-5\right)\left(y+4\right)=-7\\ \Rightarrow\left(x-5\right),\left(y+4\right)\inƯ\left(-7\right)=\left\{1;-1;7;-7\right\}\)

Ta có bảng:

Vậy \(\left(x;y\right)=\left(6;-11\right),\left(4;3\right),\left(12;-5\right),\left(-2;-3\right)\)

e) 

\(x-\left(17-8\right)=5+\left(10-3x\right)\\ \Rightarrow x-9=5+10-3x\\ \Rightarrow x+3x=5+10+9\\ \Rightarrow4x=24\\ \Rightarrow x=\dfrac{24}{4}=6\)

Vậy \(x=6\)

a)  3x – 15 = 25 – 5x 

=> 3x + 5x = 25 + 15

=> 8x = 40

=> x = 5

 b) 3x - 17 = 2x – 7     

=> 3x - 2x = -7 + 17

=> x = 10

 c) 2x – 17 =  – (3x – 18)

=> 2x - 17 = -3x + 18

=> 2x + 3x = 18 + 17

=> 5x = 35

=> x = 7

d) 3x – 14 = 2(x – 9) + 1

=> 3x - 14 = 2x - 18 + 1

=> 3x - 2x = -18 + 1 + 14

=> x = -3

f) (x – 5)² = 9          

\(\Rightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

a) Ta có: \(3x-15=25-5x\)

\(\Leftrightarrow3x-15-25+5x=0\)

\(\Leftrightarrow8x-40=0\)

\(\Leftrightarrow8x=40\)

hay x=5

Vậy: x=5

b) Ta có: \(3x-17=2x-7\)

\(\Leftrightarrow3x-17-2x+7=0\)

\(\Leftrightarrow x-10=0\)

hay x=10

Vậy: x=10

c) Ta có: \(2x-17=-\left(3x-18\right)\)

\(\Leftrightarrow2x-17=-3x+18\)

\(\Leftrightarrow2x-17+3x-18=0\)

\(\Leftrightarrow5x-35=0\)

\(\Leftrightarrow5x=35\)

hay x=7

Vậy: x=7

d) Ta có: \(3x-14=2\left(x-9\right)+1\)

\(\Leftrightarrow3x-14=2x-18+1\)

\(\Leftrightarrow3x-14-2x+18-1=0\)

\(\Leftrightarrow x+3=0\)

\(\Leftrightarrow x=-3\)

Vậy: x=-3

f) Ta có: \(\left(x-5\right)^2=9\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

Vậy: \(x\in\left\{2;8\right\}\)

Bài 2. Tìm x, biết :                                

a) \(3x-15=25-5x\)

\(\Leftrightarrow8x=40\)

\(\Leftrightarrow x=5\)

Vậy x = 5

b) \(3x-17=2x-7\)

\(\Leftrightarrow x=10\)

Vậy x = 10

c) \(2x-17=-\left(3x-18\right)\)

\(\Leftrightarrow2x-17=18-3x\)

\(\Leftrightarrow5x=35\)

\(\Leftrightarrow x=7\)

Vậy x = 7

d) \(3x-14=2\left(x-9\right)+1\)

\(\Leftrightarrow3x-14=2x-18+1\)

\(\Leftrightarrow3x-14=2x-17\)

\(\Leftrightarrow x=-3\)

Vậy x = -3

e) \(\left(x-5\right)^2=9\)

\(\Rightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

Vậy x = {8; 2}

d) Ta có: \(-8+\left(-14\right)+34+\left(-12\right)\)

\(=-8-14+34-12\)

\(=-20+20\)

\(=-0\)

e) Ta có: \(\left(-7\right)+\left(-20\right)+57+\left(-30\right)\)

\(=\left(-7+57\right)+\left(-20-30\right)\)

\(=50-50=0\)

f) Ta có: \(300-\left(-180\right)-120-42\)

\(=300+180-120-42\)

\(=258+60=318\)

d, Ta có : \(\left(-8\right)+\left(-14\right)+34+\left(-12\right)\)

\(=-\left(8+12\right)+34-14=-20+20=0\)

e, Ta có : \(\left(-7\right)+\left(-20\right)+57+\left(-30\right)\)

\(=-\left(30+20\right)+57-7=-50+50=0\)

f, Ta có : \(300-\left(-180\right)-120-42=318\)

d,=-8-14+34-12=(-8+34)-(14+12)

=26-26=0

e,=-7-20+57-30=(-7+57)-(20+30)

=50-50=0

f,=300+180-120-42=300+40-42=298

Ta có: (x-y)(x+y)=2022

nên \(\left(x-y\right)\left(x+y\right)⋮2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-y⋮2\\x+y⋮2\end{matrix}\right.\)

Khi đó, x và y sẽ có cùng tính chẵn hoặc lẻ

nên x+y và x-y đều là số chẵn

\(\Leftrightarrow\left(x+y\right)\left(x-y\right)⋮4\)

mà 2022 không chia hết cho 4

nên không có x,y thỏa mãn bài toán

\(21.7^2-11\left(-7\right)^2+90.7^2+51.\left(-10\right)^2\)

\(=21.7^2-11.7^2+90.7^2+51.10^2\)

\(=7^2\left(21-11+90\right)+51.10^2\)

\(=7^2.100+51.100\)

\(=100\left(7^2+51\right)\)

= 100. (49 + 51)

= 100.100

= 10000

21.7 2 − 11 ( − 7 ) 2 + 90.7 2 + 51. ( − 10 ) 2

= 21.7 2 − 11.7 2 + 90.7 2 + 51.10 2

= 7 2 ( 21 − 11 + 90 ) + 51.10 2

= 7 2 .100 + 51.100 = 100 ( 7 2 + 51 )

= 100. (49 + 51)

= 100.100 = 10000

$x_{52}$ ở đâu vậy bạn? Bạn xem lại đề.

\(\left(-2\right)+4+\left(-6\right)+8+....+\left(-18\right)\)

\(=\left(-2+4\right)+\left(-6+8\right)+\left(-10+12\right)+\left(-14+16\right)+\left(-18\right)\)

\(=2+2+2+2-18=8-18=-10\)

(-2)+4+(-6)+8+...+(-18)

=(-2+4)+(-6+8)+(-10+12)+(-14+16)+(-18)

=2        +  2     +     2        +    2        +(-18)

=8                                                     +(-18)

=-10

2.

a, x-13=-46

=>x=(-46)+13

=>x=33

b, 4x-6=22

=>4x=22+6

=>4x=28

=>x=28:4

=>x=7

3.

a, 32=2⁵

48=2⁴.3

=>ƯCLN(32,48)=2⁴=16

16=2⁴

72=2³.3²

=>ƯCLN(16,72)=2³=8

b,

24=2³.3

60=2².3.5

=>BCNN(24,60)=2³.3.5=120

72=2³.3²

180=2².3².5

=>BCNN(72,180)=2³.3².5=360

a) x - 13  =  -   46 

    x         =  - ( 46 + 13 )                                

    x         =  - 59   

Chắc vậy

2a/ -33

2b/  7

3a/ 16

       8

3b/ 120

       360