Bài 3
1) \(28-3\left(x+4\right)=13\)
\(3\left(x+4\right)=28-13\)
\(3\left(x+4\right)=15\)
\(x+4=15:3\)
\(x+4=5\)
\(x=5-4\)
\(x=1\)
2) \(450:\left(x-209\right)+230=280\)
\(450:\left(x-209\right)=280-230\)
\(450:\left(x-209\right)=50\)
\(x-209=450:50\)
\(x-209=9\)
\(x=9+209\)
\(x=218\)
3) \(5^{23}:5^{21}+3\left(132-x\right)=106\)
\(5^2+3\left(132-x\right)=106\)
\(25+3\left(132-x\right)=106\)
\(3\left(132-x\right)=106-25\)
\(3\left(132-x\right)=81\)
\(132-x=81:3\)
\(132-x=27\)
\(x=132-27\)
\(x=105\)
4) \(x\inƯ\left(90\right)\) và \(x\le30\)
Ta có: \(Ư\left(90\right)=\left\{1;2;3;5;6;9;10;15;18;30;45;90\right\}\)
Do \(x\le30\) nên \(x=1;x=2;x=3;x=5;x=6;x=9;x=10;x=15;x=18;x=30\)
5) \(x⋮105;x⋮75;x⋮60;x< 3000\)
\(\Rightarrow\) \(x\) là bội chung của 105; 75; 60
105 = 3 . 5 . 7
75 = 3 . 52
60 = 22 . 3 . 5
BCNN(105; 75; 60) = 22 . 3 . 52 . 7 = 2100
BC(105; 75; 60) = B(2100) = {0; 2100; 4200; ...}
Do \(x< 3000\Rightarrow x=0;x=2100\)
6) \(96⋮x;102⋮x;168⋮x\) và \(x\) lớn nhất
\(\Rightarrow x=ƯCLN\left(96;102;168\right)\)
96 = 25 . 3
102 = 2 . 3 . 17
168 = 23 . 3 . 7
\(\Rightarrow x=ƯCLN\left(96;102;168\right)=2.3=6\)
7) \(x⋮78;x⋮39;x⋮65\); \(x\) nhỏ nhất và khác 0
\(\Rightarrow x\) là BCNN(78; 39; 65)
78 = 2 . 3 . 13
39 = 3 . 13
65 = 5 . 13
BCNN(78; 39; 65) = 2 . 3 . 5 . 13 = 390
Vậy \(x\) = 390
