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d) \(\dfrac{2}{19}.\dfrac{-4}{7}+\dfrac{2}{19}.\dfrac{-3}{7}\)
= \(\dfrac{2}{19}.\left(\dfrac{-4}{7}+\dfrac{-3}{7}\right)\)
=\(\dfrac{2}{19}.\left(-1\right)=\dfrac{-2}{19}\)
c) C=(151515/161616 + 17^9/17^10)-(1500/1600 - 1616/1717)
=(15/16 + 1/17)-(15/16 - 16/17)
= 15/16 ( 1/17 + 16/17)
=15/16 . 1 = 15/16
Bài 9:
1, -15 + 17 - 22 + 15 - 17 + 22
= -(15 - 15) + (17 - 17) - (22 - 22)
= 0 + 0 + 0
= 0
2, 45 - 58 + (-45) + (+58) - 3
= 45 - 58 - 45 + 58 - 3
= (45 - 45) - (58 - 58) - 3
= 0 - 0 - 3
= -3
c) |-x+7|=24
⇒\(\left[{}\begin{matrix}-x+7=24\\-x+7=-24\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-17\\x=31\end{matrix}\right.\)
d) |x+8|+15=0
|x+8|=0-15
|x+8|=-15
⇒x=∅
e) |x|+|x-3|=0
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
c: Ta có: \(\left|-x+7\right|=24\)
\(\Leftrightarrow\left[{}\begin{matrix}7-x=24\\7-x=-24\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-17\\x=31\end{matrix}\right.\)
Bài 1:
a) Ta có: \( \left|x+2\right|=\left|3-2x\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=2x-3\\x+2=3-2x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2x=-3-2\\x+2x=3-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=-5\\3x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{1}{3}\end{matrix}\right.\)
b) Ta có: \(\left|2x-4\right|=\left|3-x\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-4=3-x\\2x-4=x-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x+x=3+4\\2x-x=-3+4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=7\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=1\end{matrix}\right.\)
c) \(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{12}\le x\le\dfrac{7}{10}+\dfrac{27}{6}\)
\(\Leftrightarrow\dfrac{2}{3}\le x\le\dfrac{26}{5}=5,2\), mà \(x\in Z\)
\(\Rightarrow x\in\left\{1;2;3;4;5\right\}\)
d) \(-\dfrac{31}{14}+\dfrac{115}{131}+\dfrac{111}{74}\le x\le\dfrac{6}{36}+\dfrac{9}{27}+\dfrac{48}{96}\)
\(\Leftrightarrow\dfrac{150}{917}\le x\le1\) , mà \(x\in Z\)
\(\Rightarrow x=1\)
\(\left(\dfrac{2}{4}+0,5+25\%\right).2\dfrac{2}{3}\\ =\left(\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{4}\right).\dfrac{8}{3}\\ =\dfrac{5}{4}.\dfrac{8}{3}\\ =\dfrac{10}{3}\)
1