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1200/[(20*x+40)/x]=30
(20*x+40)/x=1200/30
20+40/x=40
40/x=40-20
40/x=20
x=40/20
x=2

a: Ta có: \(150=2\cdot3\cdot5^2;84=2^2\cdot3\cdot7;30=2\cdot3\cdot5\)
Do đó: ƯCLN(150;84;30)\(=2\cdot3=6\)
150⋮x; 84⋮x; 30⋮x
=>x∈ƯC(150;84;30)
=>x∈Ư(6)
mà x<16
nên x∈{1;-1;2;-2;3;-3;6;-6}
b: Ta có: \(15=3\cdot5;14=2\cdot7;20=2^2\cdot5\)
Do đó: BCNN(15;14;20)\(=2^2\cdot3\cdot5\cdot7=4\cdot3\cdot5\cdot7=20\cdot21=420\)
x⋮15; x⋮14; x⋮20
=>x∈BC(15;14;20)
=>x∈B(420)
mà 400<=x<=1200
nên x∈{420;840}
c: 9⋮x+1
=>x+1∈{1;-1;3;-3;9;-9}
=>x∈{0;-2;2;-4;8;-10}
d: 2x+7⋮x-2
=>2x-4+11⋮x-2
=>11⋮x-2
=>x-2∈{1;-1;11;-11}
=>x∈{3;1;13;-9}

a: Ta có: \(150=5^2\cdot2\cdot3;84=2^2\cdot3\cdot7;30=2\cdot3\cdot5\)
Do đó: ƯCLN(150;84;30)\(=2\cdot3=6\)
150⋮x; 84⋮x; 30⋮x
=>x∈ƯC(150;84;30)
=>x∈Ư(6)
mà x<16
nên x∈{1;-1;2;-2;3;-3;6;-6}
b: \(15=3\cdot5;14=2\cdot7;20=2^2\cdot5\)
Do đó: BCNN(15;14;20)\(=2^2\cdot3\cdot5\cdot7=4\cdot3\cdot5\cdot7=12\cdot35=420\)
x⋮15; x⋮14; x⋮20
=>x∈BC(15;14;20)
=>x∈B(420)
mà 400<=x<=1200
nên x∈{420;840}
c: 9⋮x+1
=>x+1∈{1;-1;3;-3;9;-9}
=>x∈{0;-2;2;-4;8;-10}
d: 2x+7⋮x-2
=>2x-4+11⋮x-2
=>11⋮x-2
=>x-2∈{1;-1;11;-11}
=>x∈{3;1;13;-9}

a: Ta có: \(150=5^2\cdot2\cdot3;84=2^2\cdot3\cdot7;30=2\cdot3\cdot5\)
Do đó: ƯCLN(150;84;30)\(=2\cdot3=6\)
150⋮x; 84⋮x; 30⋮x
=>x∈ƯC(150;84;30)
=>x∈Ư(6)
mà x<16
nên x∈{1;-1;2;-2;3;-3;6;-6}
b: \(15=3\cdot5;14=2\cdot7;20=2^2\cdot5\)
Do đó: BCNN(15;14;20)\(=2^2\cdot3\cdot5\cdot7=4\cdot3\cdot5\cdot7=12\cdot35=420\)
x⋮15; x⋮14; x⋮20
=>x∈BC(15;14;20)
=>x∈B(420)
mà 400<=x<=1200
nên x∈{420;840}
c: 9⋮x+1
=>x+1∈{1;-1;3;-3;9;-9}
=>x∈{0;-2;2;-4;8;-10}
d: 2x+7⋮x-2
=>2x-4+11⋮x-2
=>11⋮x-2
=>x-2∈{1;-1;11;-11}
=>x∈{3;1;13;-9}

a; 90 ⋮ \(x\) và 26 ⋮ \(x\) ⇒ \(x\in\) ƯC(90; 26)
90 = 2.32.5; 26 = 2.13
ƯCLN(90; 26) = 2
\(x\in\) Ư(2) = {-2; -1; 1; 2}
Vì 10 < \(x\) < 30 nên \(x\) \(\in\) \(\varnothing\)
c; 150 ⋮\(x\) ; 84 ⋮ \(x\); 30 ⋮ \(x\)
\(x\in\) ƯC(150; 84; 30)
150 = 2.3.52; 84 = 22.3.7; 30 = 2.3.5
ƯCLN(150;84;30) = 2.3 = 6
\(x\in\) Ư(6) = { 1; 2; 3; 6}
Vì 0 < \(x< 16\)
Vậy \(x\in\) {1; 2; 3; 6}

\(\left(27.700-45.20\right)\div\left(45-40+35-30+25-20+15-10+5\right)\)
\(=\)\(\left(27.100-45.20\right)\div25\)
\(=\)\(\left(27.35.20-45.20\right)\div25\)
\(=\)\(\left[\left(27.35-45\right).20\right]\div25\)
\(=\)\(18000\div25\)
\(=\)\(750\)

1200/[(20*x+40)/x]=30
(20*x+40)/x=1200/30
20+40/x=40
40/x=40-20
40/x=20
x=40/20
x=2