a) 450 – ( 25 – 10) = 450 – 15

                   = 435

450 – 25 – 10 = 425 – 10

                   = 415

b) 180 : 6 : 2 = 30 : 6

                   = 15

180 : ( 6 : 2 ) = 180 : 3

                   = 60

c) 410 – (50 +30) = 410 -80

                   = 330

410 - 50 + 30 = 360 + 30

                   = 390

d) 16 x (6 : 3) = 16 x 2

                   = 32

16 x 6 : 3 = 96 : 3

                   = 32

x+450=600+180

x+450=780

x=780-450

x=330

x + 450 = 600 + 180

x + 450 = 780

x = 780 - 450

x = 330

⇒ 180 - x +45  = 120:2

⇒ 225 - x = 60

⇒ x= 225-60

⇒ x = 165

180-(x-45):2=120

        (x-45):2=180-120

         (x-45):2=60

         x-45=60.2

         x-45=120

            x=120+45

            x=165

\(450:\left(x-19\right)=15\)

\(=>x-19=450:15=30\)

\(=>x=30+19=49\)

\(\left(x-1\right)\left(y-2\right)=2=1.2=-1.-2\)

\(x-1=1=>x=2\)

\(y-2=1=>y=3\)

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

\(y-2=2=>y=4\)

\(x-1=-1=>x=0\)

\(y-2=-1=>y=1\)

\(x-1=-2=>x=-1\)

\(y-2=-2=>y=0\)

Câu C làm tương tự câu b

Câu a:

252 = 2^2.3^2.7; 858 = 2.3.11.13; 156 = 2^2.3.13

ƯCLN(252; 858; 156) = 2.3 = 6

ƯC(252; 858; 156) = Ư(6) = {6; 3; 2; 1}

b, Tìm số tự nhiên x biết 400 chia x thì dư 40; còn 450 chia x thì dư Giải:

Vì: 400 : x dư 40 nên:

(400 - 40) ⋮ x

360 ⋮ x(1)

Vì 450 : x dư 18 nên:

(450 - 18) ⋮ x

432 ⋮ x (2)

Kết hợp (1) và (2) ta có:

x ∈ ƯC(360; 432)

360 = 2^3.3^2.5; 432 = 2^4.3^3

ƯCLN(360; 432) = 2^3.3^2 = 72

x ∈ Ư(72) = {1; 2; 3; 4; 6; 8; 9; 12; 18; 24;36; 72} (3)

Vì 400 : x dư 40 nên x ≥ 40 + 1 = 41

Vì 450 : x dư 18 nên x ≥ 18 + 1 = 19

Nên x ≥ 41 (4)

Kết hợp (3) và (4) ta có:

x = 72

a, \(252=2^2.3.31\)

\(858=2.3.11.13\)

\(156=2^2.3.13\)

\(ƯCLN\left(252,858,156\right)=2.3=6\)

b, Vì : 400 chia cho x thì dư 40

\(\Rightarrow400-40⋮x\left(x>40\right)\)

\(\Rightarrow360⋮x\) (1)

Vì : 450 chia cho x thì dư 18

\(\Rightarrow450-18⋮x\left(x>18\right)\)

\(\Rightarrow432⋮x\) (1)

Từ (1) và (2) \(\Rightarrow x\inƯC\left(360,432\right)\left(x>40\right)\)

\(360=2^3.3^2.5\)

\(432=2^4.3^2\)

\(ƯCLN\left(360,432\right)=2^3.3^2=72\)

\(\RightarrowƯC\left(360,432\right)=Ư\left(72\right)=\left\{1;2;3;4;6;8;9;12;18;24;36;72\right\}\)

Mà : \(x>40\Rightarrow x=72\)

Vậy x = 72

\(450:\left(x-19\right)=50\\ \Leftrightarrow x-19=5\\ \Leftrightarrow x=24\)

\(2\left(x-52\right)=2.23+20\\ \Leftrightarrow2\left(x-52\right)=66\\ \Leftrightarrow x-52=33\\ \Leftrightarrow x=85\)

\(10-\left(x-3\right):2=72-100\\ \Leftrightarrow10-\left(x-3\right):2=-28\\ \Leftrightarrow10-\left(x-3\right)=-56\\ \Leftrightarrow x-3=66\\ \Leftrightarrow x=69\)

1.x-19=450:50

   x-19=9

  x      =9+19

 x        =28

2. 2(x-51)=46+20

    2(x-51)=66

       x-51=66:2

       x-51=33

       x      =33+51

       x       =84

\(a,\Leftrightarrow x+9=39\Leftrightarrow x=30\\ b,\Leftrightarrow73-x=69\Leftrightarrow x=4\\ c,\Leftrightarrow x+7=38\Leftrightarrow x=31\\ d,\Leftrightarrow x+4=178\Leftrightarrow x=174\\ e,\Leftrightarrow2\left(x-51\right)=16+20=36\Leftrightarrow x-51=18\Leftrightarrow x=69\\ f,\Leftrightarrow x-19=9\Leftrightarrow x=28\\ g,\Leftrightarrow4\left(x-3\right)=49-1=48\Leftrightarrow x-3=12\Leftrightarrow x=15\)

a) 45 - ( x + 9 ) = 6

45 - x = 6 + 9

45 - x = 15

x = 45 - 15

x = 30

b) 89 - ( 73 - x ) = 20

89 - x = 20 + 73

89 - x = 93

x = 93 - 89

x = 4

c) 198 - ( x + 4 ) = 120

198 - x = 120 + 4

198 - x = 124

x = 198 - 124

x = 74

d) ( x + 7 ) - 25 = 13

x - 25 = 13 + 7

x - 25 = 20

x = 20 + 25

x = 45

e) 2 ( x - 51 ) = 2.2³ + 20

2 ( x - 51 ) = 64 + 20

2 ( x - 51 ) = 84

x - 51 = 84 - 2

x - 51 = 82

x = 82 + 51

x = 133

f) 450 : ( x - 19 ) = 50

450 : x = 50 - 19

450 : x = 41

x = 450 : 41

x = 24