Câu hỏi của Đặng Hoài An

Question

Tìm x sao cho x thuộc tập hợp số nguyên:

1) x - 43 = (35 - x) - 48

2) 305 - x + 14 = 48 + (x + 23)

3) - (x - 6 + 85) = (x + 51) - 54

4) - (35 - x - 37 - x) = 33 - x

5) 13 - | x | = | -4 |

6) | x...

Trần Khánh Quỳnh · Accepted Answer

dài quá à :(Câu trả lời: dài quá à :(

Ayano Yuuki · Answer

1) x - 43 = (35 - x) - 48 => x + x = 35 - 48 + 43 => x + x = 30 => x = 30 : 2 => x = 15 2) 305 - x + 14 = 48 + (x + 23) => 305 - x + 14 = 48 + x + 23 => -x - x = 48 + 23 - 14 - 305 => -x - x = -248 => -x = -248 : 2 => -x = -124 => x = 124 3) - (x - 6 + 85) = (x + 51) - 54 => -x + 6 - 85 = x + 51 - 54 => -x - x = 51 - 54 + 85 - 6 => -x - x = 76 => -x = 76 : 2 => -x = 38 => x = -38 4) - (35 - x - 37 - x) = 33 - x => -35 + x + 37 + x = 33 - x => x + x + x = 33 + 35 - 37 => x + x + x = 31 => x = 31 : 3 => x $=\dfrac{31}{3}$ Vì x $\in$ Z nên không có giá trị x nào thỏa mãn trong câu này. 5) 13 - | x | = | -4 | => 13 - |x| = 4 => |x| = 13 - 4 => |x| = 9 => $\left[{}\begin{matrix}x=9\x=-9\end{matrix}\right.$ 6) | x | - 3 + 6 = 16 => |x| = 16 - 6 + 3 => |x| = 13 => $\left[{}\begin{matrix}x=13\x=-13\end{matrix}\right.$ 7) 35 - | 2x - 1 | = 14 => |2x - 1| = 35 - 14 => |2x - 1| = 21 => $\left[{}\begin{matrix}2x-1=21\2x-1=-21\end{matrix}\right.=>\left[{}\begin{matrix}2x=21+1\2x=-21+1\end{matrix}\right.=>\left[{}\begin{matrix}2x=22\2x=-20\end{matrix}\right.=>\left[{}\begin{matrix}x=22:2\x=-20:2\end{matrix}\right.=>\left[{}\begin{matrix}x=11\x=-10\end{matrix}\right.$ 8) | 3x - 2 | + 5 = 9 - x => |3x - 2| = 9 - 5 - x => |3x - 2| = 4 - x => $\left[{}\begin{matrix}3x-2=4-x\3x-2=x-4\end{matrix}\right.=>\left[{}\begin{matrix}3x+x=4+2\3x-x=-4+2\end{matrix}\right.=>\left[{}\begin{matrix}4x=6\2x=-2\end{matrix}\right.=>\left[{}\begin{matrix}x=6:4\x=-2:2\end{matrix}\right.=>\left[{}\begin{matrix}x=\dfrac{6}{4}\x=-1\end{matrix}\right.$ Vì x $\in$ Z nên x = -1. 9) x - ( -25 + 7 ) > 12 - ( 15 - 14 ) => x - (-18) > 12 - 1 => x + 18 > 11 => x > 11 - 18 => x > -7 10) | 17 + ( x - 15 ) | < 4 => $\left[{}\begin{matrix}17+\left(x-15\right)< 4\17+\left(x-15\right)< -4\end{matrix}\right.=>\left[{}\begin{matrix}x-15< 4-17\x-15< -4-17\end{matrix}\right.=>\left[{}\begin{matrix}x-15< -15\x-15< -21\end{matrix}\right.=>\left[{}\begin{matrix}x< -15+15\x< -21+15\end{matrix}\right.=>\left[{}\begin{matrix}x< 0\x< -6\end{matrix}\right.=>x< -6$ 11) x2 - 5x = 0 => x . (2 - 5) = 0 => x . (-3) = 0 => x = 0 : (-3) => x = 0 12) | x-9 | . (-8) = -16 => |x - 9| = (-16) : (-8) => |x - 9| = 3 => $\left[{}\begin{matrix}x-9=3\x-9=-3\end{matrix}\right.=>\left[{}\begin{matrix}x=3+9\x=-3+9\end{matrix}\right.=>\left[{}\begin{matrix}x=12\x=6\end{matrix}\right.$ 13) | 4 - 5x | = 24 với x < hoặc = 0 => $\left[{}\begin{matrix}4-5x=24\4-5x=-24\end{matrix}\right.=>\left[{}\begin{matrix}5x=4-24\5x=4-\left(-24\right)\end{matrix}\right.=>\left[{}\begin{matrix}5x=-20\5x=28\end{matrix}\right.=>\left[{}\begin{matrix}x=-20:5\x=28:5\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\x=\dfrac{28}{5}\end{matrix}\right.$ Vì x $\le$ 0 nên x = -4 14) x . ( x - 2 ) > 0 => $\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x< 0\x-2< 0\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x< 0\x< 2\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}x>2\x< 2\end{matrix}\right.$ 15) x . ( x - 2 ) < 0 => $\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}2>x< 0\left(loại\right)\0< x< 2\left(chọn\right)\end{matrix}\right.=>0< x< 2$ 16) (x-1) . (y+1) = 5 => $\left[{}\begin{matrix}x-1=5\y+1=1\end{matrix}\right.=>\left[{}\begin{matrix}x=5+1\y=1-1\end{matrix}\right.=>\left[{}\begin{matrix}x=6\y=0\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=1\y+1=5\end{matrix}\right.=>\left[{}\begin{matrix}x=1+1\y=5-1\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=4\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=-1\y+1=-5\end{matrix}\right.=>\left[{}\begin{matrix}x=-1+1\y=-5-1\end{matrix}\right.=>\left[{}\begin{matrix}x=0\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=-5\y+1=-1\end{matrix}\right.=>\left[{}\begin{matrix}x=-5+1\y=-1-1\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=-2\end{matrix}\right.$ 17) x . ( y +2 ) = -8 => $\left[{}\begin{matrix}x=1\y+2=-8\end{matrix}\right.=>\left[{}\begin{matrix}x=1\y=-8-2\end{matrix}\right.=>\left[{}\begin{matrix}x=1\y=-10\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-1\y+2=8\end{matrix}\right.=>\left[{}\begin{matrix}x=-1\y=8-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-1\y=4\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-8\y+2=1\end{matrix}\right.=>\left[{}\begin{matrix}x=-8\y=1-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-8\y=-1\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=8\y+2=-1\end{matrix}\right.=>\left[{}\begin{matrix}x=8\y=-1-2\end{matrix}\right.=>\left[{}\begin{matrix}x=8\y=-3\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=2\y+2=-4\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=-4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-2\y+2=4\end{matrix}\right.=>\left[{}\begin{matrix}x=-2\y=4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-2\y=2\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=4\y+2=-4\end{matrix}\right.=>\left[{}\begin{matrix}x=4\y=-4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=4\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-4\y+2=2\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=2-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=0\end{matrix}\right.$ 18) xy - 2x - 2y = 0 => x . (y - 2) - 2y = 0 => x . (y - 2) - 2y - 4 = -4 => x . (y - 2) - 2 . (y - 2) = -4 => (y - 2) . (x - 2) = -4 => $\left[{}\begin{matrix}y-2=1\x-2=-4\end{matrix}\right.=>\left[{}\begin{matrix}y=1+2\x=-4+2\end{matrix}\right.=>\left[{}\begin{matrix}y=3\x=-2\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=-1\x-2=4\end{matrix}\right.=>\left[{}\begin{matrix}y=-1+2\x=4+2\end{matrix}\right.=>\left[{}\begin{matrix}y=1\x=6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=2\x-2=-2\end{matrix}\right.=>\left[{}\begin{matrix}y=2+2\x=-2+2\end{matrix}\right.=>\left[{}\begin{matrix}y=4\x=0\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=-2\x-2=2\end{matrix}\right.=>\left[{}\begin{matrix}y=-2+2\x=2+2\end{matrix}\right.=>\left[{}\begin{matrix}y=0\x=4\end{matrix}\right.$ 19) 2x - 5 $⋮$ x - 1 => (2x - 2) - (5 - 2) $⋮$ x - 1 => 2(x - 1) - 3 $⋮$ x - 1 Vì 2(x - 1) $⋮$ x - 1 nên 3 $⋮$ x - 1 => x - 1 $\in$ Ư(3) = {-3; -1; 1; 3} => x $\in$ {-2; 0; 2; 4} P/s: Mình không bảo đảm là đúng hết nên câu nào sai thì bạn thông cảm nha~Câu trả lời: 1) x - 43 = (35 - x) - 48 => x + x = 35 - 48 + 43 => x + x = 30 => x = 30 : 2 => x = 15 2) 305 - x + 14 = 48 + (x + 23) => 305 - x + 14 = 48 + x + 23 => -x - x = 48 + 23 - 14 - 305 => -x - x = -248 => -x = -248 : 2 => -x = -124 => x = 124 3) - (x - 6 + 85) = (x + 51) - 54 => -x + 6 - 85 = x + 51 - 54 => -x - x = 51 - 54 + 85 - 6 => -x - x = 76 => -x = 76 : 2 => -x = 38 => x = -38 4) - (35 - x - 37 - x) = 33 - x => -35 + x + 37 + x = 33 - x => x + x + x = 33 + 35 - 37 => x + x + x = 31 => x = 31 : 3 => x $=\dfrac{31}{3}$ Vì x $\in$ Z nên không có giá trị x nào thỏa mãn trong câu này. 5) 13 - | x | = | -4 | => 13 - |x| = 4 => |x| = 13 - 4 => |x| = 9 => $\left[{}\begin{matrix}x=9\x=-9\end{matrix}\right.$ 6) | x | - 3 + 6 = 16 => |x| = 16 - 6 + 3 => |x| = 13 => $\left[{}\begin{matrix}x=13\x=-13\end{matrix}\right.$ 7) 35 - | 2x - 1 | = 14 => |2x - 1| = 35 - 14 => |2x - 1| = 21 => $\left[{}\begin{matrix}2x-1=21\2x-1=-21\end{matrix}\right.=>\left[{}\begin{matrix}2x=21+1\2x=-21+1\end{matrix}\right.=>\left[{}\begin{matrix}2x=22\2x=-20\end{matrix}\right.=>\left[{}\begin{matrix}x=22:2\x=-20:2\end{matrix}\right.=>\left[{}\begin{matrix}x=11\x=-10\end{matrix}\right.$ 8) | 3x - 2 | + 5 = 9 - x => |3x - 2| = 9 - 5 - x => |3x - 2| = 4 - x => $\left[{}\begin{matrix}3x-2=4-x\3x-2=x-4\end{matrix}\right.=>\left[{}\begin{matrix}3x+x=4+2\3x-x=-4+2\end{matrix}\right.=>\left[{}\begin{matrix}4x=6\2x=-2\end{matrix}\right.=>\left[{}\begin{matrix}x=6:4\x=-2:2\end{matrix}\right.=>\left[{}\begin{matrix}x=\dfrac{6}{4}\x=-1\end{matrix}\right.$ Vì x $\in$ Z nên x = -1. 9) x - ( -25 + 7 ) > 12 - ( 15 - 14 ) => x - (-18) > 12 - 1 => x + 18 > 11 => x > 11 - 18 => x > -7 10) | 17 + ( x - 15 ) | < 4 => $\left[{}\begin{matrix}17+\left(x-15\right)< 4\17+\left(x-15\right)< -4\end{matrix}\right.=>\left[{}\begin{matrix}x-15< 4-17\x-15< -4-17\end{matrix}\right.=>\left[{}\begin{matrix}x-15< -15\x-15< -21\end{matrix}\right.=>\left[{}\begin{matrix}x< -15+15\x< -21+15\end{matrix}\right.=>\left[{}\begin{matrix}x< 0\x< -6\end{matrix}\right.=>x< -6$ 11) x2 - 5x = 0 => x . (2 - 5) = 0 => x . (-3) = 0 => x = 0 : (-3) => x = 0 12) | x-9 | . (-8) = -16 => |x - 9| = (-16) : (-8) => |x - 9| = 3 => $\left[{}\begin{matrix}x-9=3\x-9=-3\end{matrix}\right.=>\left[{}\begin{matrix}x=3+9\x=-3+9\end{matrix}\right.=>\left[{}\begin{matrix}x=12\x=6\end{matrix}\right.$ 13) | 4 - 5x | = 24 với x < hoặc = 0 => $\left[{}\begin{matrix}4-5x=24\4-5x=-24\end{matrix}\right.=>\left[{}\begin{matrix}5x=4-24\5x=4-\left(-24\right)\end{matrix}\right.=>\left[{}\begin{matrix}5x=-20\5x=28\end{matrix}\right.=>\left[{}\begin{matrix}x=-20:5\x=28:5\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\x=\dfrac{28}{5}\end{matrix}\right.$ Vì x $\le$ 0 nên x = -4 14) x . ( x - 2 ) > 0 => $\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x< 0\x-2< 0\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x< 0\x< 2\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}x>2\x< 2\end{matrix}\right.$ 15) x . ( x - 2 ) < 0 => $\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.=>\left[{}\begin{matrix}2>x< 0\left(loại\right)\0< x< 2\left(chọn\right)\end{matrix}\right.=>0< x< 2$ 16) (x-1) . (y+1) = 5 => $\left[{}\begin{matrix}x-1=5\y+1=1\end{matrix}\right.=>\left[{}\begin{matrix}x=5+1\y=1-1\end{matrix}\right.=>\left[{}\begin{matrix}x=6\y=0\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=1\y+1=5\end{matrix}\right.=>\left[{}\begin{matrix}x=1+1\y=5-1\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=4\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=-1\y+1=-5\end{matrix}\right.=>\left[{}\begin{matrix}x=-1+1\y=-5-1\end{matrix}\right.=>\left[{}\begin{matrix}x=0\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x-1=-5\y+1=-1\end{matrix}\right.=>\left[{}\begin{matrix}x=-5+1\y=-1-1\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=-2\end{matrix}\right.$ 17) x . ( y +2 ) = -8 => $\left[{}\begin{matrix}x=1\y+2=-8\end{matrix}\right.=>\left[{}\begin{matrix}x=1\y=-8-2\end{matrix}\right.=>\left[{}\begin{matrix}x=1\y=-10\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-1\y+2=8\end{matrix}\right.=>\left[{}\begin{matrix}x=-1\y=8-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-1\y=4\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-8\y+2=1\end{matrix}\right.=>\left[{}\begin{matrix}x=-8\y=1-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-8\y=-1\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=8\y+2=-1\end{matrix}\right.=>\left[{}\begin{matrix}x=8\y=-1-2\end{matrix}\right.=>\left[{}\begin{matrix}x=8\y=-3\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=2\y+2=-4\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=-4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=2\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-2\y+2=4\end{matrix}\right.=>\left[{}\begin{matrix}x=-2\y=4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-2\y=2\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=4\y+2=-4\end{matrix}\right.=>\left[{}\begin{matrix}x=4\y=-4-2\end{matrix}\right.=>\left[{}\begin{matrix}x=4\y=-6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}x=-4\y+2=2\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=2-2\end{matrix}\right.=>\left[{}\begin{matrix}x=-4\y=0\end{matrix}\right.$ 18) xy - 2x - 2y = 0 => x . (y - 2) - 2y = 0 => x . (y - 2) - 2y - 4 = -4 => x . (y - 2) - 2 . (y - 2) = -4 => (y - 2) . (x - 2) = -4 => $\left[{}\begin{matrix}y-2=1\x-2=-4\end{matrix}\right.=>\left[{}\begin{matrix}y=1+2\x=-4+2\end{matrix}\right.=>\left[{}\begin{matrix}y=3\x=-2\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=-1\x-2=4\end{matrix}\right.=>\left[{}\begin{matrix}y=-1+2\x=4+2\end{matrix}\right.=>\left[{}\begin{matrix}y=1\x=6\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=2\x-2=-2\end{matrix}\right.=>\left[{}\begin{matrix}y=2+2\x=-2+2\end{matrix}\right.=>\left[{}\begin{matrix}y=4\x=0\end{matrix}\right.$ hoặc => $\left[{}\begin{matrix}y-2=-2\x-2=2\end{matrix}\right.=>\left[{}\begin{matrix}y=-2+2\x=2+2\end{matrix}\right.=>\left[{}\begin{matrix}y=0\x=4\end{matrix}\right.$ 19) 2x - 5 $⋮$ x - 1 => (2x - 2) - (5 - 2) $⋮$ x - 1 => 2(x - 1) - 3 $⋮$ x - 1 Vì 2(x - 1) $⋮$ x - 1 nên 3 $⋮$ x - 1 => x - 1 $\in$ Ư(3) = {-3; -1; 1; 3} => x $\in$ {-2; 0; 2; 4} P/s: Mình không bảo đảm là đúng hết nên câu nào sai thì bạn thông cảm nha~

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