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Bài 1:
1) \(\left|x-15\right|+x-15=0\)\(\Leftrightarrow\)\(\left|x-15\right|=15-x\)
+ Với \(x\ge15\forall x\)\(\Leftrightarrow\)\(x-15\ge0\forall x\)\(\Rightarrow\)\(\left|x-15\right|=x-15\)
\(\Rightarrow x-15=15-x\)
\(\Leftrightarrow2x=30\)
\(\Leftrightarrow x=15\)( thỏa mãn điều kiện )
+ Với \(x< 15\forall x\)\(\Leftrightarrow\)\(x-15< 0\forall x\)\(\Rightarrow\)\(\left|x-15\right|=-\left(x-15\right)=15-x\)
\(\Rightarrow15-x=15-x\)
\(\Leftrightarrow0x=0\)( Vô số các giá trị. Điều kiện: \(x< 15\))
Vậy \(x\le15\)
2) \(7x.\left(2+x\right)-7x.\left(x+3\right)=14\)
\(\Leftrightarrow7x.\left(2+x-x-3\right)=14\)
\(\Leftrightarrow-7x=14\)
\(\Leftrightarrow x=-2\)( thỏa mãn )
Vậy \(x=-2\)
Bài 2:
1) Ta có: \(A=-3x^3-2x^2+x-14\)
\(\Leftrightarrow A=-\left(3x^3+6x^2\right)+\left(4x^2+8x\right)-\left(7x+14\right)\)
\(\Leftrightarrow A=-3x^2.\left(x+2\right)+4x.\left(x+2\right)-7.\left(x+2\right)\)
\(\Leftrightarrow A=\left(x+2\right).\left(-3x^2+4x-7\right)\)
+ Thay \(x=-3\)vào biểu thức A, ta có:
\(A=\left(-3+2\right).\left(-3.9-12-7\right)\)
\(\Leftrightarrow A=\left(-1\right).\left(-46\right)\)
\(\Leftrightarrow A=46\)
Vậy \(A=46\)
2) Ta có: \(B=2xy-3x+2y\)
+ Thay \(x=-2,x=-5\)vào biểu thức B, ta có:
\(B=2.\left(-2\right).\left(-5\right)-3.\left(-2\right)+2.\left(-5\right)\)
\(\Leftrightarrow B=20+6-10\)
\(\Leftrightarrow B=16\)
Vậy \(B=16\)
a ) -2. ( x +6 ) + 6. ( x -10 ) =8
-2.x + (-2).6 + 6x - 6.10 = 8
-2x + (-12) + 6x -60 = 8
(-2x+6x) + (-12) -60=8
4x + ( -72) = 8
4x = 8 - ( -72 )
4x = 8 + 72
4x = 80
x = 80 : 4
x = 20
a,\(15-\left(-4-x\right)=6\)
\(\Leftrightarrow-4-x=15-6\)
\(\Leftrightarrow-4-x=9\)
\(\Leftrightarrow x=-4-9\)
\(\Leftrightarrow x=-13\)
b,\(-30+\left(25-x\right)=-1\)
\(\Leftrightarrow25-x=-1-\left(-30\right)\)
\(\Leftrightarrow25-x=29\)
\(\Leftrightarrow x=25-29=-4\)
c,\(x-\left(12-25\right)=-8\)
\(\Leftrightarrow x+13=-8\)
\(\Leftrightarrow x=-21\)
e,\(x-5=1\Rightarrow x=6\)
g,\(x+30=-4\)
\(\Leftrightarrow x=-4-30\)
\(\Leftrightarrow x=-34\)
h,\(x-\left(-24\right)=3\)
\(\Leftrightarrow x+24=3\)
\(\Leftrightarrow x=3-24\)
\(\Leftrightarrow x=-21\)
i,\(\left(x+5\right)+\left(x-9\right)=x+2\)
\(\Leftrightarrow x+5+x-9-x-2=0\)
\(\Leftrightarrow x-6=0\)
\(\Leftrightarrow x=6\)
k,\(\left(27-x\right)+\left(15+x\right)=x-24\)
\(\Leftrightarrow27-x+15+x-x+24=0\)
\(\Leftrightarrow-x+66=0\)
\(\Leftrightarrow-x=-66\)
\(\Leftrightarrow x=66\)
a) 15-(-4-x)=6
15 + 4 + x = 6
19 + x = 6
x = 6 - 19
x = 6 + ( -19 )
x = -13
b) -30+( 25- x ) =-1
25- x = -1 - ( - 30 )
25- x = -1 + 30
25- x =29
x = 25 - 29
x = 25 + ( -29 )
x = -4
c) x- ( 12-25) =-8
x - ( - 13 ) = -8
x + 13 = -8
x = -8 - 13
x = -8 + ( -13 )
x = - 21
d) ( x-29 ) - (17- 38 ) = -9
( x-29) - (-21 ) = -9
x -29 = -9 + ( -21 )
x -29 = -30
x = -30 + 29
x = -1
e) x-5=1
x = 1 + 5
x = 6
g) x + 30 = -4
x = -4 - 30
x = -4 + ( -30 )
x = -34
h) x- ( -24 ) = 3
x = 3 + ( -24 )
x = -21
l) 22- ( - x ) = 12
-x = 22 - 12
-x = 10
x = -10
i) ( x + 5 ) + ( x - 9 ) = x + 2
x + 5 + x - 9 = x + 2
x + x + ( 5 - 9 ) = x + 2
x + x + ( -4 ) = x + 2
x + x = x + 2 - ( -4 )
x + x = x + 2 + 4
x + x =x + 6
=> x = 6
\(4^{15}.5^{30}=\left(2^2\right)^{15}.5^{30}=2^{30}.5^{30}=\left(2.5\right)^{30}=10^{30}\)
\(27^{16}.9^{10}=\left(3^3\right)^{16}.\left(3^2\right)^{10}=3^{48}.3^{20}=3^{68}\)
\(\frac{72^3.54^2}{1084}=\frac{\left(2^3.3^2\right)^3.\left(2.3\right)^2}{2^2.271}=\frac{2^2.2^9.3^6.3^2}{2^2.271}=\frac{2^9.3^8}{271}\)
\(\frac{3^{10}.11+3^{10}.5}{39.24}=\frac{3^{10}.16}{39.24}=\frac{3.3.3^8.2.8}{3.13.3.8}=\frac{3^8.2}{13}\)(Cái này đoán đề thoi, thật sự câu này viết đề chả hiểu gì)
a) 4 . x mũ 3 + 15 = 47
4 . x mũ 3 = 32
x mũ 3 = 8
x mũ 3 = 2 mũ 3
=> x = 2
4.x^3+15 = 47
4.x^3=47-15
4. x^3=32
x^3=32:4
X^3=8
x^3 = 2^3
=> x = 3
a) 2(4x-8)-7(3+x)=|-4|.(3-2)
8x-16-21-7x=4
8x-7x=4+16+21
x=41
Vậy x=41
b) 8(x-|-7|)-6(x-2)=|-8|.6-50
8x-56-6x+12=8.6-50
8x-6x=48-50+56-12
2x=42
x=42:2
x=21
Vậy x=21
c) -7(5-x)-2(x-10)=15
-35+7x-2x+20=15
7x-2x=15+35-20
5x=30
x=30:5
x=6
Vậy x=6
d) 4(x-1)-3(x-2)=-|-5|
4x-4-3x+6=-5
4x-3x=-5+4-6
x=-7
Vậy x=-7
e) -4(x+1)+(89x-3)=24
-4x-4+89x-3=24
-4x+89x=24+4+3
85x=31
x=31/85
f) 5(x-30)-2(x+6)=9
5x-150-2x-12=9
5x-2x=9+150+12
3x=171
x=171:3
x=57
Vậy x=57
g) -3(x-5)+6(x+2)=9
-3x+15+6x+12=9
-3x+6x=9-15-12
3x=-18
x=-18:3
x=-6
Vậy x=-6
h) 7(x-9)-5(6-x)=-6+11x
7x-63-30+5x=-6+11x
7x+5x-11x=-6+62+30
x=86
Vậy x=86
k) 10(x-7)-8(x+5)=6.(-5)+24
10x-70-8x-40=-30+24
10x-8x=-30+24+70+40
2x=104
x=104:2
x=52
Vậy x=52
a. 250 - 10 ( 24 - 3x) : 15 = 244
10 ( 24 - 3x) : 15 = 250 - 244
10 ( 24 - 3x) : 15 = 6
10 ( 24 - 3x) = 15 .6
10 ( 24 - 3x) = 90
( 24 - 3x) = 90 : 10
( 24 - 3x) = 9
3x = 24 - 9
3x =15
x = 15 : 3
x = 5
b. 30 - [ 4 ( x - 2 ) + 15 ] =3
[ 4 ( x - 2 ) + 15 ] = 30 - 3
4 ( x - 2 ) + 15 = 27
4 ( x - 2 ) = 27 - 15
4 ( x - 2 ) = 12
x - 2 = 12 : 4
x - 2 = 3
x = 3 + 2
x = 5