Giải thích các bước giải:

Bài 1: Tính tổng sau một cách hợp lí:

a)−7105−(155−7105)+355

= −7105+6950+355

= 355−155

= 200

b) (35−815)−(795−65)

= −780−730

= −1510

c) 5−197−2015−2015

= −192−2015−2015

= −2207−2015

= −4222

d) 4567=1234−4567−66

⇔ 4567=−3333−66

⇔ 4567=−3399 (không TM)

e) 2004−15+54−2004−54

= 1989+54−2004−54

= 2043−2004−54

= 39−54

= −15

f) −45789−357−45789+57

= −46146−45789+57

= −91935+57

= −91878

g) 1259−1409−12+1259+1409

= −150−12+1259+1409

= −162+1259+1409

= 1097+1409

= 2506

h) 2750−1229+2750−[−438−29−438]

= 2750−1229+2750−(−467−438)

= 2750−1229+2750+905

= 1521+2750+905

= 4271+905

= 5176

i) −5+−37−45+151−−37+151

= −5−37−45+151+37+151

= −42−45+151+37+151

= −87+151+37+151

= 64+37+151

= 101+151

= 252

k) 53−145−359−53+145−259

= −92−359−53+145−259

= −451−53+145−259

= −504+145−259

= −359−259

= −618

l) −81−132−547+181−132−53 

= −213−547−181−132−53

= −760−181−132−53

= −941−132−53

= −1073−53

= −1126

m) 50−2016+50−118+2016−18

= −1966+50−118+2016−18

= −1916−118+2016−18

= −2034+2016−18

= −18−18

= −36

n) 254−49−75+254−175+549

= 205−75+254−175+549

= 130+254−175+549

= 384−175+549

= 209+549

= 758

p) 173−536+173−[29−29+526]

= 173−536+173−526

= −363+173−526

= −190−526

= −716

q) −[−171+171+223]−[172−105+172]+223

= −223−(172−105+172)+223

= −223−(67+172)+223

= −223−239+223

= −462+223

= −239

Bài 2: Tìm số nguyên x, biết:

a) 25−(25−x)=12+(42−65)

⇔ 25−25+x=12+42−65

⇔ x=12+42−65

⇔ x=54−65

⇔ x=−11

b) 5+|x+3|=9

⇔ ∣x+3∣=9−5

⇔ ∣x+3∣=4

TH1: x+3=4

⇔ x=4−3

⇔ x=1

TH2: −(x+3)=4

⇔ −x−3=4

⇔ −x=4+3

⇔ −x=7

⇔ x=−7

vậy phương trình này có nghiệm là x= {1 ; −7}.

c) 31−(17+x)=18

⇔ 31−17−x=18

⇔ 14−x=18

⇔ −x=18−14

⇔ −x=4

⇔ x=−4

d) x−(−25+x)=13−x

⇔ x+25−x=13−x

⇔ x+25=13

⇔ x=13−25

⇔ x=−12

xin hay nhất! :)))

Câu 1:

a. `- 7105  - ( 155 - 7105 ) + 355`

`= - 7105 - 155 + 7105 + 355`

`= [ 7105 + ( - 7105 ) ] + 355 - 155`

`= 0 + 355 - 155`

`= 355 - 155`

`= 200`

b. `( 35 - 815 ) - ( 795 - 65 )`

`= 35 - 815 - 795 - 65`

`= - 780 - ( - 795 - 65 )`

`= - 780 - 860`

`= - 1640`

c. `5 - 197 - 2015 - 2015`

`= - 192 - (2015 - 2015 )`

`= - 192 - 0`

`= - 192`

d. `4567 +1234 - 4567--66`

`=(4567-4567)+(1234--66)`

`=0 + 1300`

`=1300`

e. `2004 -15 +54-2004 -54`

`=(2004-2004)+(54-54)-15`

`=0+0-15`

`=-15`

f. `(-45789+45789)-(357-57)`

`=0 -300`

`= -300`

g. `1259 - 1409 - 12 + 1259 + 1409`

`=(1259+1259)+(1409-1409)`

`= 2.1259+0`

`= 2518`

h. `2750 - 1229 + 2750 - (-438 - 29 - 438)`

`= 2.2750+(29-1229)+438.2`

`= 5500-1200+876`

`= 5176`

i. `-5 + (-37) - 45 + 151 - (-37) + 151`

`= -5-45+(37-37)+2.151`

`= -50+0+302`

`= 252`

k. `53 - 145 - 359 - 53 + 145 - 259`

`= (53-53)+(145-145)-(359+259)`

`= 0+0-618`

`= -618`

l. `- 81 - 132 - 547 + 181 - 132 - 53`

`= [(-81) + 181 ] - ( 547 + 53 ) - ( 132 + 132 )`

`= 100 - 600 - 264`

`= (-500) - 264`

`= -764`

k. `254-49- 75+ 254- 175+ 549`

`=(549-49)-(175+75)+254+254`

`=500-250+254+254`

`=758254-49- 75+ 254- 175+ 549`

`=(549-49)-(175+75)+254+254`

`=500-250+254+254`

`=758`

p. `173-536+173-[29-(29+526)`

`= 173 -536 +173 -29+(29+526)`

`= 173 -536 +173 -29+29+526`

`= (173 +173) + ( -536 +526) + (-29+29)`

`= 346 - 10 + 0 `

`= 336`

q. `−[−171+171+223]−[172−105+172]+223`

`=171-171-223+172+105-172+223`

`=(171-171)+(172-172)-(223-223)`

`=0`

Câu 2:

a. `25 - (25 - x)=12 + (42 - 65)`

  `25 - 25 + x=12 + 42 - 65`

                  `x=-11`

b. `5 + |x + 3|=9`

          `|x + 3|=9 - 5`

          `|x + 3|=4`

`TH1: x + 3=4`

`⇒x=1`

`TH2: x +3=-4`

`⇒x=(-7)`

Vậy `x∈{1;-7}`

c. `31 - (17 + x)=18`

`31 - 17 - x=18`

`14 - x=18`

 `x=14 - 18`

`x=-4`

d. `x - (-25 + x)=13 - x`

  `x + 25 - x=13 - x`

  `25 =13 - x`

  `13 - x=25`

         `x=13 - 25`

         `x=-12`