Bài 7

3.

Vì x⋮7 nên x là bội của 7

B(7)={0;7;14;21;28;35;42;49;56;63;....}

mà 10 ≤ x ≤ 35 nên x ∈ {14;21;28;35}

Vậy x ∈ {14;21;28;35} thỏa mãn bài toán

MẤY PHẦN CÒN LẠI TƯƠNG TỰ ❕

\(1,2^3-5^3:5^2+12\cdot2^2\)

\(=8-5+12\cdot4=3+48=51\)

\(2)5\cdot\left\lbrack\left(85-35:7\right):8+90\right\rbrack-50\)

\(=5\cdot\left\lbrack\left(85-5\right):8+90\right\rbrack-50\)

\(=5\cdot\left(80:8+90\right)-50\)

\(=5\cdot\left(10+90\right)-50=5\cdot100-50\)

\(=500-50=450\)

\(3)2\cdot\left\lbrack\left(7-3^3:3^2\right):2^2+99\right\rbrack-100\)

\(=2\cdot\left\lbrack\left(7-3\right):4+99\right\rbrack-100\)

\(=2\cdot\left(1+99\right)-100=2\cdot100-100\)

\(=200-100=100\)

\(4)2^7:2^2+5^4:5^3\cdot2^4-3\cdot2^5\)

\(=2^5+5^2\cdot16-3\cdot32=32+25\cdot16-96\)

\(=32+400-96=336\)

\(5)5\cdot2^2\cdot2^3-4\cdot\left(5^8:5^6\right)=5\cdot2^5-4\cdot5^2\)

\(=5\cdot32-4\cdot25=160-100=60\)

\(6)\left(3^5\cdot3^7\right):3^{10}+5\cdot2^4-7^3:7\)

\(=3^{12}:3^{10}+5\cdot16-7^2=9+80-49=40\)

\(7)15:\left(3^5:3^4\right)-2^9:2^7\)

\(=15:3-4=5-4=1\)

\(8)5\cdot3^5:\left(3^8:3^5\right)-2^3\cdot5\)

\(=5\cdot3^2-40=5\cdot9-40=45-40=5\)

\(9)4\left\lbrack\left(3+3^7:3^4\right):10+97\right\rbrack-300\)

\(=4\left\lbrack\left(3+3^3\right):10+97\right\rbrack-300\)

\(=4\left\lbrack\left(3+27\right):10+97\right\rbrack-300\)

\(=4\cdot\left(3+97\right)-300=400-300=100\)

\(10)5\left\lbrack\left(92+2^5:2^2\right):5^2+2^4\right\rbrack-7^2\)

\(=5\left\lbrack\left(92+8\right):25+16\right\rbrack-49\)

\(=5\cdot\left(100:25+16\right)-49\)

\(=5\cdot\left(4+16\right)-49=100-49=51\)

\(11)3^2\cdot\left\lbrack5^2-3\right):11]-2^4+2\cdot10^3\)

\(=9\cdot\left(22:11\right)-16+2000=9\cdot2-16+2000\)

\(=18-16+2000=2002\)

\(12)2^2\cdot5\left\lbrack\left(5^2+2^3\right):11-2\right\rbrack-3^2\cdot2\)

\(=4\cdot5\left\lbrack\left(25+8\right):11-2\right\rbrack-18\)

\(=20\cdot\left(3-2\right)-18=20-18=2\)

\(13)\left(6^{2007}-6^{2006}\right):6^{2006}\)

\(=\left\lbrack6^{2006}\cdot\left(6-1\right)\right\rbrack:6^{2006}=5\)

14) \(\left(5^{2001}-5^{2000}\right):5^{2000}\)

\(=\left\lbrack5^{2000}\cdot\left(5-1\right)\right\rbrack:5^{2000}=4\)

\(15)\left(7^{2005}+7^{2004}\right):7^{2004}\)

\(=\left\lbrack7^{2004}\cdot\left(7+1\right)\right\rbrack:7^{2004}=8\)

\(16)\left(11^{2023}+11_{}^{2022}\right):11^{2022}\)

\(=\left\lbrack11^{2022}\cdot\left(11+1\right)\right\rbrack:11^{2022}=12\)

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