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a)\(18-|x|=8\Rightarrow|x|=10\Rightarrow x\in\left\{-10;10\right\}\)
b)\(|x|+42=91\Rightarrow|x|=49\Rightarrow x\in\left\{-49;49\right\}\)
c)\(|x|-\left(-54\right)=96\Leftrightarrow|x|+54=96\Rightarrow|x|=42\Rightarrow x\in\left\{-42;42\right\}\)
d)\(|x|-\left(-15\right)=47\Leftrightarrow|x|+15=47\Rightarrow|x|=32\Rightarrow x\in\left\{-32;32\right\}\)
\(a,\) nếu \(x\ge0\) nếu \(x< 0\)
<=> 18 - / x / = 8 <=> 18 - / x / = 8
<=> 18 - x = 8 <=> 18 - ( - x ) = 8
<=> x = 18 - 8 <=> 18 + x = 8
<=> x = 10 <=> x = 8 - 18
<=> x = -10
câu b,c,d tương tự nha
a) 5x - 14 = x - 34
5x - x = -34 + 14
4x = -20
x = -20 : 4
x = -5
b) x - 3 - (3x + 2) = -15
x - 3 - 3x - 2 = -15
x - 3x = -15 + 3 + 2
-2x = -10
x = (-10) : (-2)
x = 5
c) 2(x - 12) + 19 = x + (-34)
2x - 24 + 19 = x + (-34)
2x - x = -34 + 24 - 19
x = -29
d) 2(x - 33) - 3(x - 43) = 96 - 115
2x - 66 - 3x + 129 = 96 - 115
2x - 3x = 96 - 115 + 66 - 129
-x = -82
x = 82
e) 2x + 3 - 9x = -11
2x - 9x = -11 - 3
-7x = -14
x = (-14) : (-7)
x = 2
f) -(x + 3 - 84) = (x + 70 - 71) - 6
-x - 3 + 84 = x + 70 - 71 - 6
-x - x = 70 - 71 - 6 - 84
-2x = -91
x = (-91) : (-2)
x = 45,5
a: (x-3)(y+1)=15
=>\(\left(x-3\right)\left(y+1\right)=1\cdot15=15\cdot1=\left(-1\right)\cdot\left(-15\right)=\left(-15\right)\cdot\left(-1\right)=3\cdot5=5\cdot3=\left(-3\right)\cdot\left(-5\right)=\left(-5\right)\cdot\left(-3\right)\)
=>(x-3;y+1)\(\in\){(1;15);(15;1);(-1;-15);(-15;-1);(3;5);(5;3);(-3;-5);(-5;-3)}
=>(x,y)\(\in\){(4;14);(18;0);(2;-16);(-12;-2);(6;4);(8;2);(0;-6);(-2;-4)}
b: Sửa đề:\(m=1+3+3^2+3^3+...+3^{99}+3^{100}\)
\(m=1+3+\left(3^2+3^3+3^4\right)+\left(3^5+3^6+3^7\right)+...+\left(3^{98}+3^{99}+3^{100}\right)\)
\(=4+3^2\left(1+3+3^2\right)+3^5\left(1+3+3^2\right)+...+3^{98}\left(1+3+3^2\right)\)
\(=4+13\left(3^2+3^5+...+3^{98}\right)\)
=>m chia 13 dư 4
\(m=1+3+3^2+...+3^{99}+3^{100}\)
\(=1+\left(3+3^2+3^3+3^4\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)
\(=1+3\left(1+3+3^2+3^3\right)+3^5\left(1+3+3^2+3^3\right)+...+3^{97}\left(1+3+3^2+3^3\right)\)
\(=1+40\left(3+3^5+...+3^{97}\right)\)
=>m chia 40 dư 1
a) 416 + ( x-45 )= 387
416-45+x=387
x=387-(416-45)
x=16
b) 11-(x+84)=97
11-x-84=97
-x=84-11+97
-x=170
x=-170
c) -(x+84)+213=-16
-x-84+213=-16
-x=-16-213+84
-x=-145
x=145
d)x+(-35)=18
x-35=18
x=53
e) -2x-(-17)=15
-2x+17=15
-2x=-2
x=1
P/s tham khảo nha
A) 416 + (X-45) =387
416+X-45= 387
416-45+X=387
371+X=387
X=387-371
X=16
B) 11-(X+84)=97
11-X-84=97
11-84-X=97
-73-X=97
X=-73-97
X=-170
C) -(X+84) +213=-16
-X-(84-213) =-16
-X-(-129)=-16
-X=(-16)+(-129)
-X= -145
X=145
D) X+(-35)=18
X=18-(-35)
X=53
E) -2X-(-17) =15
-2X+17=15
-2X=15-17
-2X=-2
X=-2:-2
X=1
a, - ( x + 84 ) + 213 = -16
=> - ( x + 84 ) = -16 - 213
=> - ( x + 84 ) =-229
=> x + 84 = 229
=> x = 145
b. x + ( -35 ) = 18
=> x = 18 - ( -35 )
=> x = 18 + 35
=> x = 53
c. -2x - ( - 17 ) = 15
=> -2x = 15 + ( -17)
=> -2x = -2
=> x = 1
\(a,-\left(x+84\right)+213=-16\)
\(x+84=213+16\)
\(x+84=229\)
\(x=229-84\)
\(x=145\)
\(b,x+\left(-35\right)=18\)
\(x=18+35\)
\(x=53\)
\(c,-2x-\left(-17\right)=15\)
\(-2x+17=15\)
\(2x=17-15\)
\(2x=2\)
\(x=1\)
\(x+\left(-32\right)=-84-\left(-46\right)\)
\(x-32=-84+46\)
\(x-32=-38\)
\(x=-38+32\)
\(x=-6\)
\(453+x=-443-\left(-199\right)\)
\(453+x=-443+199\)
\(453+x=-244\)
\(x=-244-453\)
\(x=-697\)
\(\left|-x+7\right|=24\)
\(\Rightarrow\hept{\begin{cases}-x+7=24\\-x+7=-24\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=7-24\\x=7+24\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=-17\\x=31\end{cases}}\)
a) x + 118 = 218
x = 218 – 118
x = 100
b) 18 – x = -17
X = 18 – (-17)
X = 35
c) (-18) – x = -17
X = (-18) – (-17)
X = -1
d)124 + (118 – x) = 217
118 – x = 93
X = 118 – 93
X = 25
e) (3x – 6).3 = 34
(3x – 6).3 = 81
3x – 6 = 27
3x = 33
ð X = 11
g) 23.(42 – x) = 46
42 – x = 2
ð X = 40
h) 84 – (3x + 8) = 34
3x + 8 = 84 – 34
3x + 8 = 50
3x = 50 – 8
3x = 42
X = 42 : 3
ð X = 14
i) 3.(2x + 1) – 19 = 14
3.(2x + 1) = 14 + 19
3.(2x + 1) = 33
2x + 1 = 33 : 3
2x + 1 = 11
2x = 11 – 1
2x = 10
X = 10 : 2
ð X = 5
k) 6x – 302 = 23.5
6x – 302 = 40
6x = 40 + 302
6x = 342
X = 342 : 6
ð X = 57
m) (x – 1)2 = 81
(x – 1)2 = 92
ð X – 1 = 9
ð X = 9 + 1
ð X = 10
n) 2x+1 – 5 = 27
2x+1 = 27 + 5
2x+1 = 32
2x+1 = 25
ð X = 4
a) \(\left(2x-18\right):\left(-10\right)-34=2\)
\(\Rightarrow\left(2x-18\right):\left(-10\right)=2+34\)
\(\Rightarrow\left(2x-18\right):\left(-10\right)=36\)
\(\Rightarrow2x-18=36\cdot\left(-10\right)\)
\(\Rightarrow2x-18=-360\)
\(\Rightarrow2x=-360+18\)
\(\Rightarrow2x=-342\)
\(\Rightarrow x=-342:2\)
\(\Rightarrow x=-171\)
b) \(120:\left(5x+20\right)-45=75\)
\(\Rightarrow120:\left(5x+20\right)=75+45\)
\(\Rightarrow120:\left(5x+20\right)=120\)
\(\Rightarrow5x+20=120:120\)
\(\Rightarrow5x+20=1\)
\(\Rightarrow5x=1-20\)
\(\Rightarrow5x=-19\)
\(\Rightarrow x=-\dfrac{19}{5}\)
a) X=27
b) X=8
c) X=-33