Tìm các số nguyên x biết: a) (-8).x = (-10).(-2) - 4; b) (-9).x + 3 = (-2).(-7) + 16; c) 22.x+100 = 210; d) (-12).x - 34 = 2
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a, 3 + x = 8
x = 8 - 3
x = 5
b, x + 4 = 0
x = 0 - 4
x = - 4
c x + 8 = 3
x = 3 - 8
x = -5
d 2 + x = -10
x = -10 - 2
x = - 12
a) \(10⋮\left(x-1\right)\) (đkxđ \(x\ne1\))
\(\Rightarrow x-1\in\left\{-1;1;-2;2;-5;5;-10;10\right\}\)
\(\Rightarrow x\in\left\{0;2;-1;3;-4;6;-9;11\right\}\)
b) \(\left(x+5\right)⋮\left(x-2\right)\left(đkxđ,x\ne2\right)\)
\(\Rightarrow\left(x+5\right)-\left(x-2\right)⋮\left(x-2\right)\)
\(\Rightarrow x+5-x+2⋮\left(x-2\right)\)
\(\Rightarrow7⋮\left(x-2\right)\)
\(\Rightarrow x-2\in\left\{-1;1;-7;7\right\}\)
\(\Rightarrow x\in\left\{1;3;-5;9\right\}\)
c) \(\left(3x+8\right)⋮\left(x-1\right)\left(đkxd,x\ne1\right)\)
\(\Rightarrow\left(3x+8\right)-3\left(x-1\right)⋮\left(x-1\right)\)
\(\Rightarrow3x+8-3x+3⋮\left(x-1\right)\)
\(\Rightarrow11⋮\left(x-1\right)\)
\(\Rightarrow x-1\in\left\{-1;1;-11;11\right\}\)
\(\Rightarrow x\in\left\{0;2;-10;12\right\}\)
a) x∈{0;2;−1;3;−4;6;−9;11}
b) x∈{1;3;−5;9}
c) x ∈ {0;2;−10;12}
\(a,x+21=6\\ \Rightarrow x=-15\\ b,x-10=-8\\ \Rightarrow x=2\\ c,\left(-8\right)x=\left(-7\right)\left(-6\right)\\ \Rightarrow\left(-8\right)x=42\\ \Rightarrow x=-4\\ d,20+8\left(x+3\right)=5^2.4\\ \Rightarrow20+8\left(x+3\right)=25.4\\ \Rightarrow20+8\left(x+3\right)=100\\ \Rightarrow8\left(x+3\right)=80\\ \Rightarrow x+3=10\\ \Rightarrow x=7\)
\(a.x+21=6\\ x=6-21\\ x=-15\\ b.x-10=-8\\ x=-8+10\\ x=2\\ c.-8x=-7.\left(-6\right)-2\\ -8x=42-2\\ -8x=40\\ x=40:\left(-8\right)\\ x=-5\)
\(d.20+8\left(x+3\right)=5^2.4\\ 20+8x+24=25.4\\ 44+8x=100\\ 8x=100-44\\ 8x=56\\ x=56:8\\ x=7\)
\(\text{(x+2)(y-3)=5 }\)
\(\Rightarrow\)x+2;y-3\(\in\)Ư(5)
Mà Ư(5)={1;5;-1;-5}
Có bảng:
Th1:
x+2=1;y-3=6
=>x=-3
y=9
Tương tự 3 trường hợp còn lại
a) 2(x+1)-4 = 5x+7
2x + 2 - 4 - 5x=7
-3x = 7 - 2 + 4
-3x = 9
x = 9 : (-3)
x = -3
b) 10 = 10 + 9 + 8 + ... + x
=> 9 + 8 + ... + x = 0
=> x = -9