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2:
a: =>2(x+1)=26
=>x+1=13
=>x=12
b: =>(6x)^3=125
=>6x=5
=>x=5/6(loại)
c: =>\(7\cdot3^x\cdot\dfrac{1}{3}+11\cdot3^x\cdot3=318\)
=>3^x=9
=>x=2
d: -2x+13 chia hết cho x+1
=>-2x-2+15 chia hết cho x+1
=>15 chia hết cho x+1
=>x+1 thuộc {1;3;5;15}
=>x thuộc {0;2;4;14}
e: 4x+11 chia hết cho 3x+2
=>12x+33 chia hết cho 3x+2
=>12x+8+25 chia hết cho 3x+2
=>25 chia hết cho 3x+2
=>3x+2 thuộc {1;-1;5;-5;25;-25}
mà x là số tự nhiên
nên x=1
1:
a: Đặt A=2^2024-2^2023-...-2^2-2-1
Đặt B=2^2023+2^2022+...+2^2+2+1
=>2B=2^2024+2^2023+...+2^3+2^2+2
=>B=2^2024-1
=>A=2^2024-2^2024+1=1
c: \(=\dfrac{3^{12}\cdot2^{11}+2^{10}\cdot3^{12}\cdot5}{2^2\cdot3\cdot3^{11}\cdot2^{11}}=\dfrac{2^{10}\cdot3^{12}\left(2+5\right)}{2^{13}\cdot3^{12}}\)
\(=\dfrac{7}{2^3}=\dfrac{7}{8}\)
\(\left(a\right)\frac{3}{7}-\left(\frac{-2}{7}\right)=\frac{3}{7}+\frac{2}{7}=\frac{5}{7}\)
\(\left(b\right)\frac{-13}{11}+\frac{6}{22}-\frac{36}{33}=\frac{-39}{33}+\frac{9}{33}-\frac{36}{33}=\frac{-66}{33}=-2\)
\(a,\frac{3}{7}-\frac{-2}{7}=\frac{3-\left(-2\right)}{7}=\frac{3+2}{7}=\frac{5}{7}\)
\(b,-\frac{13}{11}+\frac{6}{22}-\frac{36}{33}=-\frac{13}{11}+\frac{3}{11}-\frac{12}{11}=\frac{-13+3-12}{11}=-\frac{22}{11}=-2\)
\(c,-\frac{6}{17}-\frac{5}{-12}+\frac{3}{81}=-\frac{6}{17}+\frac{5}{12}+\frac{1}{27}=\frac{-6.27.12+5.17.27+17.12}{17.12.27}=\frac{185}{1836}\)
\(\frac{2}{70}-\frac{9}{-24}+\frac{-5}{42}=\frac{1}{35}+\frac{3}{8}-\frac{5}{42}=\frac{1.24+105.3-5.20}{840}=\frac{239}{840}\)
Câu 5:
a: \(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
\(=31\left(-18-81-1\right)\)
\(=31\cdot\left(-100\right)=-3100\)
b: \(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)
\(=\left(-12\right)\left(47+52+1\right)\)
\(=-12\cdot100=-1200\)
c: \(13\cdot\left(23+22\right)-3\cdot\left(17+28\right)\)
\(=13\cdot45-3\cdot45\)
\(=45\cdot10=450\)
d: \(-48+48\left(-78\right)+48\left(-21\right)\)
\(=48\left(-1-78-21\right)\)
\(=48\left(-100\right)=-4800\)
Câu 4:
a: \(\left(-6-2\right)\left(-6+2\right)=\left(-8\right)\cdot\left(-4\right)=32\)
b: \(\dfrac{\left(7\cdot3-3\right)}{-6}=\dfrac{21-3}{-6}=\dfrac{18}{-6}=-3\)
c: \(\left(-5+9\right)\cdot\left(-4\right)=4\cdot\left(-4\right)=-16\)
d: \(\dfrac{72}{-6\cdot2+4}=\dfrac{72}{-12+4}=\dfrac{72}{-8}=-9\)
a: =-48+27+56-48-27-36
=-96+20
=-76
b: =23-57+57-33=-10
c: =-98+12-159-12-41
=-98-200
=-298
a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)
= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)
= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)
= 1 - 1 - \(\dfrac{11}{25}\)
= - \(\dfrac{11}{25}\)
b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)
= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))
= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)
= - \(\dfrac{499}{35}\)
a) 220 - [32 . 33 - (12 - 70) 2]
= 220 - [9 . 27 - (12 - 1)2]
= 220 - [9 . 27 - 112]
= 220 - [9 . 27 - 121]
= 220 - [243 - 121]
= 220 - 122
= 98
b) [504 - (52 . 8 + 70) : 33 + 6] : 125
= [504 - (25 . 8 + 70) : 27 + 6] : 125
= [504 - (200 + 70) : 27 + 6] :125
= [504 - 270 : 27 + 6] : 125
= [504 - 10 + 6] : 125
= [494 + 6] : 125
= 500 : 125
= 4
c) 27 . 23 + 4 . 32 - 5 . 120
= 27 . 8 + 4 . 9 - 5 . 1
= 216 + 36 - 5
= 252 - 5
= 247
d) 316 - (5. 2 . 22 + 24) : 23 - 3 . 23
= 316 - (5 . 2 . 4 + 16) : 8 - 3 . 8
= 316 - (40 + 16) : 8 - 3 . 8
= 316 - 56 : 8 - 3 . 8
= 316 - 7 - 3 . 8
= 316 - 7 - 24
= 309 - 24
= 285