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Bài 1:
\(101\cdot125+101\cdot25-101\cdot50\)
\(=101\cdot\left(125+25-50\right)\)
\(=101\cdot100\)
\(=10100\)
Bài 2:
\(76\cdot115+56\cdot24+59\cdot24\)
\(=76\cdot115+24\cdot\left(56+59\right)\)
\(=76\cdot115+24\cdot115\)
\(=115\cdot\left(76+24\right)\)
\(=115\cdot100\)
\(=11500\)
Bài 10:
a: 2x-3 là bội của x+1
=>\(2x-3⋮x+1\)
=>\(2x+2-5⋮x+1\)
=>\(-5⋮x+1\)
=>\(x+1\in\left\{1;-1;5;-5\right\}\)
=>\(x\in\left\{0;-2;4;-6\right\}\)
b: x-2 là ước của 3x-2
=>\(3x-2⋮x-2\)
=>\(3x-6+4⋮x-2\)
=>\(4⋮x-2\)
=>\(x-2\inƯ\left(4\right)\)
=>\(x-2\in\left\{1;-1;2;-2;4;-4\right\}\)
=>\(x\in\left\{3;1;4;0;6;-2\right\}\)
Bài 14:
a: \(4n-5⋮2n-1\)
=>\(4n-2-3⋮2n-1\)
=>\(-3⋮2n-1\)
=>\(2n-1\inƯ\left(-3\right)\)
=>\(2n-1\in\left\{1;-1;3;-3\right\}\)
=>\(2n\in\left\{2;0;4;-2\right\}\)
=>\(n\in\left\{1;0;2;-1\right\}\)
mà n>=0
nên \(n\in\left\{1;0;2\right\}\)
b: \(n^2+3n+1⋮n+1\)
=>\(n^2+n+2n+2-1⋮n+1\)
=>\(n\left(n+1\right)+2\left(n+1\right)-1⋮n+1\)
=>\(-1⋮n+1\)
=>\(n+1\in\left\{1;-1\right\}\)
=>\(n\in\left\{0;-2\right\}\)
mà n là số tự nhiên
nên n=0
[(x+34)-50].2=56
`<=>(x+34-50).2=56
`<=>(x-16).2=56
`<=>2x-32=56
`<=>2x=56+32
`<=>2x=88
Ta có: \(\left(x+34-50\right)\cdot2=56\)
\(\Leftrightarrow x-16=28\)
hay x=44
a: Ta có: \(100-7\left(x-5\right)=58\)
\(\Leftrightarrow7\left(x-5\right)=42\)
\(\Leftrightarrow x-5=6\)
hay x=11
b: Ta có: \(12\left(x-1\right):3=4^3+2^3\)
\(\Leftrightarrow12\left(x-1\right)=216\)
\(\Leftrightarrow x-1=18\)
hay x=19
a,91-5(5+x)=61
=>25+5x=91-61=30
=>5x=30-25=5
=>x=1
b,\([\left(x+34\right)-50]\)x2=56
=>(x+34)-50=56:2=28
=>x+34=28+50=78
=>x=78-34=44.
c,1045-\([2015-\left(3x-24\right)]\)=5
=>2015-(3x-24)=1045-5=1040
=>3x-24=2015-1040=975
=>3x=975+24=999
=>x=999:3=333
d,\([195-\left(3x-27\right)]\)x39=4212
=>195-(3x-27)=4212:39=108
=>3x-27=195-108=87
=>3x=87+27=117
=>x=39
e,30-3(x-2)=18
=>30-3x+6=18
=>30-3x=18-6=12
=>3x=30-12=18
=>x=18:3=6
a) \(...\Rightarrow5\left(5+x\right)=91-61=30\)
\(\Rightarrow\left(5+x\right)=30:5=6\Rightarrow x=6-5=1\)
b) \(...\Rightarrow\left(x+34\right)-50=56:2=28\)
\(\Rightarrow\left(x+34\right)=28+50=78\Rightarrow x=78-34=44\)
c) \(...\Rightarrow2015-\left(3x-24\right)=1045-5=1040\)
\(\Rightarrow\left(3x-24\right)=2015-1040=975\)
\(\Rightarrow3x=975+24=999\Rightarrow x=999:3=333\)
d) \(...\Rightarrow195-\left(3x-27\right)=4212:39=108\)
\(\Rightarrow\left(3x-27\right)=195-108=87\)
\(\Rightarrow3x=87+27=114\Rightarrow x=114:3=38\)
e) \(...\Rightarrow3\left(x-2\right)=30-18=12\Rightarrow x-2=12:3=4\)
\(\Rightarrow x=4+2=6\)
Bài 2:
a: Ta có: \(2^{x+1}\cdot3^y=12^x\)
\(\Leftrightarrow2^{x+1}\cdot3^y=2^{2x}\cdot3^x\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1=2x\\x=y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
a, 91 - 5 . ( 5 + x ) = 61
5 . (5+x)=91-61
5 . (5+x)=30
5+x=30:5
5+x=6
x=6-5
x=1
Bài 1. Tìm số tự nhiên x biết:
a, 91 - 5 . ( 5 + x ) = 61
5(5 + x) = 91 - 61
5(5 + x) = 30
5 + x = 30 : 5
5 + x = 6
x = 6-5
x= 1
b, ( x+ 34 ) - 50 = 56 : 2
( x + 34 ) - 50 = 28
x + 34 = 28 + 50
x + 34 = 68
x= 78 - 34
x = 44
Tk mk nha