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Bài 1:
a: 2x+3=15
=>2x=15-3=12
=>\(x=\frac{12}{2}=6\)
b: 28-3x=13
=>\(3x=28-13=15\)
=>\(x=\frac{15}{3}=5\)
c: \(\left(x-1954\right)\cdot5=50\)
=>x-1954=50:5=10
=>x=10+1954=1964
d: 30(60-x)=30
=>60-x=1
=>x=60-1=59
Bài 2:
a: x+99:3=55
=>x+33=55
=>x=55-33=22
b: (x-25):15=20
=>\(x-25=20\cdot15=300\)
=>x=300+25=325
c: \(7\left(3x-15\right)=42\)
=>\(3x-15=\frac{42}{7}=6\)
=>3x=15+6=21
=>\(x=\frac{21}{3}=7\)
d: \(x\left(x+1\right)=2+4+6+\cdots+2500\)
=>\(x\left(x+1\right)=2\left(1+2+3+\cdots+1250\right)\)
=>\(x\left(x+1\right)=2\cdot1250\cdot\frac{1251}{2}=1250\cdot1251\)
=>\(x^2+x-1250\cdot1251=0\)
=>(x+1251)(x-1250)=0
=>\(\left[\begin{array}{l}x+1251=0\\ x-1250=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-1251\\ x=1250\end{array}\right.\)
Bài 1:
a: \(46\cdot99=46\cdot\left(100-1\right)=46\cdot100-46\)
=4600-46
=4554
b: \(47\cdot98=47\cdot\left(100-2\right)=47\cdot100-47\cdot2\)
=4700-94
=4604
c: \(18\cdot19=18\left(20-1\right)=18\cdot20-18\)
=360-18
=342
d: \(24\cdot198=24\left(200-2\right)\)
\(=24\cdot200-24\cdot2\)
=4800-48
=4752
Bài 2:
a: \(1800\cdot5=18\cdot100\cdot5=90\cdot100=9000\)
b: \(36\cdot25=25\cdot4\cdot9=100\cdot9=900\)
c: 36600:50=3660:5=732
d: 220000:5000=220:5=44
c: \(\left(x-1\right)^3=\left(-9\right)^3\)
=>x-1=-9
=>x=-9+1=-8
f: \(3x-2^3=7+\left(-9\right)\)
=>3x-8=7-9=-2
=>3x=-2+8=6
=>x=2
Bài 7: Ta có: \(a\cdot b=ƯCLN\left(a;b\right)\cdot BCN\mathbb{N}\left(a;b\right)\)
=>\(a\cdot b=10\cdot900=9000\)
ƯCLN(a;b)=10
=>a⋮10; b⋮10
ab=9000
mà a⋮10 và b⋮10 và a<b
nên (a;b)∈{(10;900);(20;450);(30;300);(50;180);(60;150);(90;100)}
mà ƯCLN(a;b)=10
nên (a;b)∈{(10;900);(20;450);(50;180);(90;100)}
Bài 5:
ƯCLN(a;b)=6
=>a⋮6; b⋮6
ab=216
mà a⋮6; b⋮6
nên (a;b)∈{(6;36);(12;18);(18;12);(36;6)}
Bài 4: Gọi hai số tự nhiên cần tìm là a,b
ƯCLN(a;b)=5
=>a⋮5; b⋮5
Ta có: ab=300
mà a⋮5; b⋮5
nên (a;b)∈{(5;60);(60;5);(10;30);(30;10);(15;20);(20;15)}
Bài 1:
a: ƯCLN(a;b)=6
=>a⋮6 và b⋮6
a+b=96
mà a⋮6 và b⋮6
nên (a;b)∈{(6;90);(90;6);(12;84);(84;12);(18;78);(78;18);(24;72);(72;24);(30;66);(66;30);(36;60);(60;36);(42;54);(54;42);(48;48)}
mà ƯCLN(a;b)=6
nên (a;b)∈{(6;90);(90;6);(18;78);(78;18);(30;66);(66;30);(42;54);(54;42)}
b: ƯCLN(a;b)=4
=>a⋮4 và b⋮4
a+b=16
mà a⋮4; b⋮4 và a>b
nên (a;b)∈{(12;4);(8;8)}
mà ƯCLN(a;b)=4
nên (a;b)=(12;4)
d: \(48\cdot26+24\cdot148\)
\(=48\cdot26+48\cdot74\)
\(=48\cdot\left(26+74\right)=48\cdot100=4800\)
e: \(23\cdot48+92\cdot88\)
\(=23\cdot4\cdot12+92\cdot88\)
\(=92\cdot12+92\cdot88=92\cdot100=9200\)
b: \(89\cdot25+89\cdot74+89\)
\(=89\cdot\left(25+74+1\right)\)
\(=89\cdot100=8900\)
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
Gọi tổng chi phí cho chuyến đi là x(đồng)
(Điều kiện: x>0)
Số tiền mỗi bạn phải đóng ban đầu là \(\frac{x}{40}\) (đồng)
Số tiền mỗi bạn phải đóng thực tế là \(\frac{x}{36}\) (đồng)
Mỗi bạn tham gia còn lại phải đóng thêm 25000 đồng nên ta có:
\(\frac{x}{36}-\frac{x}{40}=25000\)
=>\(\frac{x}{360}=25000\)
=>\(x=25000\cdot360=9000000\) (đồng)
vậy: Tổng chi phí cho chuyến đi là 9000000(đồng)











Giúp tui đi🙏🏻
Em ơi, em làm được câu nào và cần hỗ trợ câu nào nhỉ?
hoa cả mắt-_-
Bài 8:
a: \(\frac{x}{5}=\frac25\)
=>\(x=5\cdot\frac25=2\)
b: \(\frac38=\frac{6}{x}\)
=>\(x=6\cdot\frac83=2\cdot8=16\)
c: \(\frac19=\frac{x}{27}\)
=>\(x=27\cdot\frac19=\frac{27}{9}=3\)
d: \(\frac{4}{x}=\frac86\)
=>\(x=4\cdot\frac68=\frac{24}{8}=3\)
e: \(\frac{3}{x-5}=\frac{-4}{x+2}\)
=>-4(x-5)=3(x+2)
=>-4x+20=3x+6
=>-4x-3x=6-20
=>-7x=-14
=>x=2
f: \(\frac{x}{-2}=\frac{-8}{x}\) (ĐKXĐ: x<>0)
=>\(\frac{x}{2}=\frac{8}{x}\)
=>\(x\cdot x=2\cdot8=16\)
=>\(x^2=16\)
=>\(\left[\begin{array}{l}x=4\left(nhận\right)\\ x=-4\left(nhận\right)\end{array}\right.\)
g: \(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-24}\)
=>\(\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-24}=-\frac12\)
=>\(\frac{x}{10}=\frac{7}{y}=\frac{z}{24}=\frac12\)
=>\(x=10\cdot\frac12=5;y=7\cdot\frac21=7\cdot2=14;z=24\cdot\frac12=\frac{24}{2}=12\)
Bài 7:
a: \(\frac{x}{5}=\frac23\)
=>\(x=5\cdot\frac23=\frac{10}{3}\)
b: \(\frac{x}{3}-\frac12=\frac15\)
=>\(\frac{x}{3}=\frac12+\frac15=\frac{7}{10}\)
=>\(x=\frac{7}{10}\cdot3=\frac{21}{10}\)
c: \(\frac{x}{5}+\frac12=\frac{6}{10}\)
=>\(\frac{x}{5}=\frac{6}{10}-\frac12=\frac{6}{10}-\frac{5}{10}=\frac{1}{10}\)
=>\(x=5\cdot\frac{1}{10}=\frac{5}{10}=\frac12\)
d: \(\frac{x}{5}+\frac12=\frac{6}{10}\)
=>\(\frac{x}{5}=\frac{6}{10}-\frac12=\frac{6}{10}-\frac{5}{10}=\frac{1}{10}\)
=>\(x=5\cdot\frac{1}{10}=\frac{5}{10}=\frac12\)
e: \(\frac{x+3}{15}=\frac13\)
=>\(\frac{x+3}{15}=\frac{5}{15}\)
=>x+3=5
=>x=5-3
=>x=2
g: \(\frac{x-12}{4}=\frac12\)
=>\(\frac{x-12}{4}=\frac24\)
=>x-12=2
=>x=12+2
=>x=14
h: \(\frac45+x=\frac23\)
=>\(x=\frac23-\frac45=\frac{10}{15}-\frac{12}{15}=-\frac{2}{15}\)
i: \(\frac34-x=\frac13\)
=>\(x=\frac34-\frac13=\frac{9}{12}-\frac{4}{12}=\frac{5}{12}\)
k: \(-\frac56-x=\frac23\)
=>\(x=-\frac56-\frac23=-\frac56-\frac46=-\frac96=-\frac32\)
l: \(x-\frac59=-\frac23\)
=>\(x=-\frac23+\frac59=\frac{-6}{9}+\frac59=-\frac19\)
m: \(\frac12x+\frac12=\frac52\)
=>\(\frac12x=\frac52-\frac12=\frac42\)
=>x=4
n: \(3\frac13+\frac56x=3\frac12\)
=>\(\frac56x=3+\frac12-3-\frac13=\frac12-\frac13=\frac16\)
=>\(x=\frac16:\frac56=\frac16\cdot\frac65=\frac15\)
o: \(\frac12-\frac23x=\frac{7}{12}\)
=>\(\frac23x=\frac12-\frac{7}{12}=\frac{6}{12}-\frac{7}{12}=-\frac{1}{12}\)
=>\(x=-\frac{1}{12}:\frac23=-\frac{1}{12}\cdot\frac32=\frac{-3}{24}=-\frac18\)
t: \(\frac34x+\frac15=\frac16\)
=>\(\frac34x=\frac16-\frac15=-\frac{1}{30}\)
=>\(x=-\frac{1}{30}:\frac34=-\frac{1}{30}\cdot\frac43=\frac{-4}{90}=-\frac{2}{45}\)
u: \(\frac38-\frac16x=\frac14\)
=>\(\frac16x=\frac38-\frac14=\frac38-\frac28=\frac18\)
=>\(x=\frac18:\frac16=\frac68=\frac34\)