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a) \(\left|\left|x-1\right|-1\right|=2\Rightarrow\orbr{\begin{cases}\left|x-1\right|-1=2\\\left|x-1\right|-1=-2\end{cases}}\Rightarrow\orbr{\begin{cases}\left|x-1\right|=3\\\left|x-1\right|=-1\left(l\right)\end{cases}}\)
TH1: x - 1 = 3
x = 4
TH2: x - 1 = - 3
x = - 2
b) Tương tự câu a.
c) \(\left|\left|2x-3\right|-x+1\right|=42-8\)
\(\left|\left|2x-3\right|-x+1\right|=34\)
TH1: \(\left|2x-3\right|-x+1=34\)
\(\left|2x-3\right|-x=33\)
Với \(x\ge\frac{3}{2}\), ta có \(2x-3-x=33\Rightarrow x=36\) (tm)
Với \(x< \frac{3}{2}\), ta có \(3-2x-x+1=34\Rightarrow-3x=30\Rightarrow x=-10\left(tm\right)\)
TH2: \(\left|2x-3\right|-x+1=-34\)
\(\left|2x-3\right|-x=-35\)
Với \(x\ge\frac{3}{2}\), ta có \(2x-3-x=-35\Rightarrow x=-32\) (l)
Với \(x< \frac{3}{2}\), ta có \(3-2x-x+1=-34\Rightarrow-3x=38\Rightarrow x=\frac{38}{3}\left(l\right)\)
d) Tương tự câu c.
Bài 1: a) min B=50 (vì |y-3|>=0) khi |y-3|=0=> y=3
b) tương tự min C=-1 khi x=100 và y=-200
a, \(\Rightarrow x-2\inƯ\left(-3\right)=\left\{\pm1;\pm3\right\}\)
| x-2 | 1 | -1 | 3 | -3 |
| x | 3 | 1 | 5 | -1 |
b, \(3\left(x-2\right)+13⋮x-2\Rightarrow x-2\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
| x-2 | 1 | -1 | 13 | -13 |
| x | 3 | 1 | 15 | -11 |
c, \(x\left(x+7\right)+2⋮x+7\Rightarrow x+7\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
| x+7 | 1 | -1 | 2 | -2 |
| x | -6 | -8 | -5 | -9 |
Bài 1:
\(\frac{x}{14}=\frac{1}{7}+\frac{-3}{14}\) \(\Rightarrow\frac{x}{14}=-\frac{1}{14}\Rightarrow x=-1\)
\(-\frac{1}{2}-x=\frac{1}{3}-\frac{1}{-4}\)\(\Leftrightarrow-x=\frac{3}{4}\Leftrightarrow x=-\frac{3}{4}\)
\(3x-30\%x=-5,4\Leftrightarrow3x-\frac{3}{10}x=-5,4\)\(\Leftrightarrow\frac{27}{10}x=-\frac{5}{4}\Rightarrow x=-\frac{25}{54}\)
Bài 3:
\(\frac{22}{3x}+\frac{8}{3}=\frac{31}{3}\Leftrightarrow\frac{22}{3x}=\frac{23}{3}\Rightarrow x=\frac{22}{23}\)
\(\frac{2}{3}+x=-45\%\Leftrightarrow\frac{2}{3}+x=-\frac{9}{20}\Leftrightarrow x=-\frac{67}{60}\)
Bài 4:
\(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{97.100}\)
\(=\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(=\frac{1}{3}.\left(1-\frac{1}{100}\right)=\frac{33}{100}\)
Bài 5:
\(\frac{64}{5}-\left(\frac{12}{3}+\frac{34}{5}\right)=\frac{64}{5}-\frac{34}{5}-\frac{12}{3}=6-4=2\)
a) X= { -1, 0, 1, 2, 3, 4 }
b) X= { -6, -5, -4, - 3, -2, -1 }
c) X= { 1, 2, 3, 4, 5, 6, 7 }
d) X= { 0, 1, 2, 3, 4, 5 }
a, X= { -1, 0, 1, 2, 3, 4 }.
b, X= { -6, -5, -4, - 3, -2, -1 }.
c, X= { 1, 2, 3, 4, 5, 6, 7 }.
d, X= { 0, 1, 2, 3, 4, 5 }.
a, !x-1!=0
\(\Rightarrow x-1=0\)
\(\Rightarrow x=0+1\)
\(\Rightarrow x=1\)
Vậy x=1
b,-11.!3x-1!=-22
\(\Rightarrow!3x-1!=-22:\left(-11\right)\)
\(\Rightarrow!3x-1!=2\)
\(\Rightarrow\orbr{\begin{cases}3x-1=2\\3x-1=-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=2+1\\3x=-2+1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=3\\3x=-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3:3\\x=-1:3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=\frac{-1}{3}\end{cases}}\)
Vậy \(\orbr{\begin{cases}x=1\\x=-\frac{1}{3}\end{cases}}\)
c, !x!<2
\(\Rightarrow x\in\left\{-1;0;1\right\}\)
Vậy \(x\in\left\{-1;0;1\right\}\)
Hok tốt nhé!!
A )
| x - 1 | = 0
x = 0 + 1
x = 1
B )
-11 . | 3x - 1 | = -22
| 3x - 1 | = -22 : ( -11 )
| 3x - 1 | = 2
3x = 2 + 1
3x = 3
x = 3 : 3
x = 1