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\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{3}{2}\right):\left(1-\frac{5}{4}\right)\)
\(\left(\frac{3x-2}{6}\right):\frac{1}{2}=\left(-\frac{5}{4}\right):\left(-\frac{1}{4}\right)\)
\(\left(\frac{3x-2}{6}\right):\frac{1}{2}=5\)
\(\left(\frac{3x-2}{6}\right)=\frac{5}{2}\)
Áp dụng công thức \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\) ta đc:
\(\Rightarrow2\left(3x-2\right)=30\)
\(\Rightarrow\left(3x-2\right)=15\)
\(\Rightarrow3x=17\)
\(\Rightarrow x=\frac{17}{3}\)
\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{3}{2}\right):\left(\frac{1-5}{4}\right)\)
\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{6}{4}\right):1\)
\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=-\frac{5}{4}:1\)
\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=-\frac{5}{4}\)
\(\frac{x}{2}-\frac{1}{3}=-\frac{5}{4}\times\frac{1}{2}\)
\(\frac{x}{2}-\frac{1}{3}=-\frac{5}{8}\)
\(\frac{x}{2}=-\frac{5}{8}+\frac{1}{3}\)
\(\frac{x}{2}=-\frac{7}{24}\)
\(x\times24=-14\)
\(x=-\frac{7}{12}\)
a) Ta có: \(\left|-5\right|+\left|x-1\right|=\left|7\right|\)
\(\Leftrightarrow\left|x-1\right|+5=7\)
\(\Leftrightarrow\left|x-1\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Vậy: \(x\in\left\{3;-1\right\}\)
b) Ta có: \(2\cdot\left|2x-4\right|-\left|-4\right|=\left|-50\right|\)
\(\Leftrightarrow4\cdot\left|x-2\right|-4=50\)
\(\Leftrightarrow4\cdot\left|x-2\right|=54\)
\(\Leftrightarrow\left|x-2\right|=\dfrac{27}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=\dfrac{27}{2}\\x-2=-\dfrac{27}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{31}{2}\left(loại\right)\\x=-\dfrac{23}{2}\left(loại\right)\end{matrix}\right.\)
Vậy: \(x\in\varnothing\)
a, | -5 | + | x-1 | = | 7 |
5 + | x - 1 | = 7
| x - 1 | = 2
TH1 x -1 = 2
x = 3
TH2 x -1 = -2
x= -1
Bài 2:
a)|x| < 3
x\(\in\){-2;-1;0;1;2}
b)|x - 4 | < 3
x\(\in\){ 6 ; 5 ; 4 ; 3 ; 2 }
c) | x + 10 | < 2
x\(\in\){ -2 ; -10 }
Bài 1:
A = 1 + 2 - 3 + 4 + 5 - 6 +...+98 - 99
A = (1 + 4 + 7 +...+97) + [(2-3)+(5-6)+...+(98-99)]
A = 1617 + [(-1)+(-1)+...+(-1)]
A = 1617 + (-49)
A = +(1617-49) = A = 1568
B = - 2 - 4 + 6 - 8 + 10 + 12 - .... + 60
B =
2)
a) \(x\in\left\{2;1;0;-1;-2\right\}\)
b) \(x\in\left\{6;-6;5;-5;4\right\}\)
c) \(x\in\left\{-9;-11;-10\right\}\)
3)
\(\left(a;b\right)\in\left\{\left(0;1\right);\left(0;-1\right);\left(1;0\right);\left(-1;0\right)\right\}\)
B1 : x + (x+1) + (x+2) + ...+ (x+35) = 0
x + x +1 + x+ 2+...+ x +35 = 0
x + x.35 + (1+2+...+35) = 0
x.36 + 630 =0
x.36 = -630
x = -630 : 36
x =- 17.5
\(a,\left(2^x-3\right)^3-59=5\)
\(\Leftrightarrow\left(2^x-3\right)^3=64=4^3\)
\(\Leftrightarrow2^x-3=4\)
\(\Leftrightarrow2^x=7\)
4-[3^3+3]=x+[13-5^2]
4-[27+3]=x+[13-25]
4-30=x+[-8]
-26=x+[-8]
[-26]+[-8]=x
-34=x
Vậy x=-34
4 - (33 + 3) = x + (13 - 52)
4 - 33 - 3 = x + 13 - 52
4 - 27 - 3 = x + 13 - 25
-26 = x - 12
-26 + 12 = x
-14 = x
=> x = -14
\(a,1+3+5+7+...+x=330\)
SSH : \((x-1):1+1=x\)
Tổng : \(\frac{(1+x)\cdot x}{2}\)
Áp dụng phương pháp đó rồi làm thôi :v
Mấy bài kia cũng tương tự như thế thui
1/2x + 1/5 = 2/3x - 1/4
=> 1/2x - 2/3x = -1/4 - 1/5
=> -1/6x = -9/20
=> x = -9/20 : (-1/6)
=> x = 27/10
\(\frac{1}{2}x+\frac{1}{5}=\frac{2}{3}x-\frac{1}{4}\)
\(\frac{1}{2}x=\frac{2}{3}x-\frac{1}{4}-\frac{1}{5}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}-\frac{2x}{3}\)
\(-\frac{x}{6}=-\frac{9}{20}\)
\(6\left(-\frac{x}{6}\right)=6\left(-\frac{9}{20}\right)\)
\(-x=-\frac{27}{10}\)
\(\Rightarrow x=-\frac{27}{10}\)