Câu 3:
a: \(\left\lbrack3\left(x+1\right)+25\right\rbrack\) ⋮5
=>3(x+1)⋮5
=>x+1⋮5
mà 9<=x<=15
nên x∈{9;14}
b: \(70=2\cdot5\cdot7;84=2^2\cdot3\cdot7;120=2^3\cdot3\cdot5\)
=>ƯCLN(70;84;120)=2
70⋮x; 84⋮x; 120⋮x
=>x∈ƯC(70;84;120)
=>x∈Ư(2)
=>x∈{1;-1;2;-2}
c: 2x+3⋮3x+2
=>6x+9⋮3x+2
=>6x+4+5⋮3x+2
=>5⋮3x+2
=>3x+2∈{1;-1;5;-5}
=>3x∈{-1;-3;3;-7}
=>3x∈{-3;3}(DO x là số nguyên)
=>x∈{-1;1}
d: \(4=2^2;7=7;8=2^3\)
=>BCNN(4;7;8)=\(2^3\cdot7=56\)
x⋮4; x⋮7; x⋮8
=>x∈BC(4;7;8)
mà x là số tự nhiên nhỏ nhất khác 0
nên x=BCNN(4;7;8)
=>x=56
e: \(24=2^3\cdot3;36=2^2\cdot3^2;160=2^5\cdot5\)
=>ƯCLN(24;36;160)=\(2^2=4\)
24⋮x; 36⋮x; 160⋮x
=>x∈ƯC(24;36;160)
mà x lớn nhất
nên x=ƯCLN(24;36;160)
=>x=4
f: x⋮25
=>x∈{0;25;50;75;100;...}
mà 0<x<100
nên x∈{25;50;75}
Câu 2:
a: \(\left\lbrack230-\left(15-5x\right)\right\rbrack\cdot3=390\)
=>230-(15-5x)=130
=>15-5x=230-130=100
=>5x=15-100=-85
=>\(x=-\frac{85}{5}=-17\)
b: \(345-5^{x-3}=14^2+24\)
=>\(345-5^{x-3}=196+24=220\)
=>\(5^{x-3}=345-220=125=5^3\)
=>x-3=3
=>x=6
c: x-[42+(-28)]=-8
=>x-(42-28)=-8
=>x-14=-8
=>x=-8+14
=>x=6
d: 720:[41-(2x-5)]=\(2^2\cdot5\)
=>720:[41-(2x-5)]=20
=>41-(2x-5)=720/20=36
=>2x-5=41-36=5
=>2x=10
=>x=5
e: 15-x=7-(-2)
=>15-x=7+2
=>15-x=9
=>x=15-9
=>x=6
f: \(\left(2x-1\right)^3=8\)
=>\(\left(2x-1\right)^3=2^3\)
=>2x-1=2
=>2x=3
=>x=1,5
