Bài 1: Tính tổng sau một cách hợp lí:
a)−7105−(155−7105)+355
b) (35−815)−(795−65)
c) 5−197−2015−2015
d) 4567=1234−4567−−66
e) 2004−15+54−2004−54
f) −45789−357−45789+57
g) 1259−1409−12+1259+1409
h) 2750−1229+2750−[−438−29−438]
i) −5+−37−45+151−−37+151
k) 53−145−359−53+145−259
l) −81−132−547+181−132−53
m) 50−2016+50−118+2016−18
n) 254−49−75+254−175+549
p) 173−536+173−[29−29+526]
q) −[−171+171+223]−[172−105+172]+223
Bài 2: Tìm số nguyên x, biết:
a) 25−(25−x)=12+(42−65)
b) 5+|x+3|=9
c) 31−(17+x)=18
d) x−(−25+x)=13−x
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`