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PN
2
VM
30 tháng 9 2019
\(\left(x+1\right).\left(x-2\right)< 0\)
\(\Rightarrow\left\{{}\begin{matrix}x+1< 0\\x-2>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\left(loại\right)\)
Hoặc:
\(\Rightarrow\left\{{}\begin{matrix}x+1>0\\x-2< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.\left(nhận\right)\)
\(\Rightarrow-1< x< 2.\)
\(\Rightarrow x\in\left\{0;1\right\}.\)
Vậy \(x\in\left\{0;1\right\}\) thì \(\left(x+1\right).\left(x-2\right)< 0.\)
Chúc bạn học tốt!
30 tháng 9 2019
(x+1).(x-2) < 0
\(\Rightarrow\left\{{}\begin{matrix}x+1>0\\x-2< 0\end{matrix}\right.hoặc\left\{{}\begin{matrix}x+1< 0\\x-2>0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.hoặc\left\{{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-1< x< 2\left(chọn\right)\\2< x< -1\left(loại\right)\end{matrix}\right.\)
Vậy -1<x<2
TV
2
18 tháng 7 2021
2: Ta có: \(5^{x-1}=5^2\)
nên x-1=2
hay x=3
5: Ta có: \(2^{2x-1}=2^{11}\)
nên 2x-1=11
\(\Leftrightarrow2x=12\)
hay x=6
8: Ta có: \(5^{2x-4}=5^{10}\)
\(\Leftrightarrow2x-4=10\)
\(\Leftrightarrow2x=14\)
hay x=7
17 tháng 7 2021
53: \(\dfrac{8^8}{4^6}=\dfrac{2^{24}}{2^{12}}=2^{12}\)
56: \(\dfrac{8^4}{2^3}=\dfrac{2^{12}}{2^3}=2^9=512\)
59: \(\dfrac{7^5}{14^3}=\dfrac{7^5}{7^3\cdot2^3}=\dfrac{1}{8}\)
62: \(\dfrac{5^5}{\left(-15\right)^4}=\dfrac{5^5}{5^4\cdot3^4}=\dfrac{5}{81}\)
17 tháng 7 2021
35: \(\dfrac{16^3}{8^3}=2^3=8\)
38: \(\dfrac{27^5}{9^4}=\dfrac{3^{15}}{3^8}=3^7\)
41: \(\dfrac{27^4}{81^5}=\dfrac{3^{12}}{3^{20}}=\dfrac{1}{3^8}\)
44: \(\dfrac{4^7}{8^3}=\dfrac{2^{14}}{2^9}=2^5=32\)0
47: \(\dfrac{64^4}{16^3}=\dfrac{2^{24}}{2^{12}}=2^{12}\)
50: \(\dfrac{9^4}{81^5}=\dfrac{3^8}{3^{20}}=\dfrac{1}{3^{12}}\)
DM
1
9 tháng 7 2017
\(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\)
\(\left(x+1\right)\left(x+3\right)=\left(0,5x+2\right)\left(2x+1\right)\)
\(x^2+4x+3=x^2+4,5x+2\)
\(x^2-x^2+4x-4,5x-2+3=0\)
\(1-0,5x=0\)
\(x=2\)
H
3 tháng 7 2021
2.
\(\dfrac{1}{3}-\dfrac{2}{5}+3x=\dfrac{3}{4}\\ \text{⇔}-\dfrac{1}{15}+3x=\dfrac{3}{4}\\ \text{⇔}3x=\dfrac{3}{4}+\dfrac{1}{15}=\dfrac{49}{60}\\ \text{⇔}x=\dfrac{49}{180}\)
4.
\(\dfrac{3}{2}-4\left(\dfrac{1}{4}-x\right)=\dfrac{2}{3}-7x\\ \text{⇔}\dfrac{3}{2}-1+4x=\dfrac{2}{3}\\ \text{⇔}4x+\dfrac{1}{2}=\dfrac{2}{3}\\ \text{⇔}4x=\dfrac{1}{6}\\ \text{⇔}x=\dfrac{1}{24}\)
6.
\(4\left(\dfrac{1}{2}-x\right)-5\left(x-\dfrac{3}{10}\right)=\dfrac{7}{4}\\ \text{⇔}2-4x-5x+\dfrac{15}{10}=\dfrac{7}{4}\\ \text{⇔}\dfrac{7}{2}-9x=\dfrac{7}{4}\\ \text{⇔}9x=\dfrac{7}{4}\\ \text{⇔}x=\dfrac{7}{36}\)
8.
\(3-2x-\dfrac{1}{3}=7x-\dfrac{1}{4}\\ \text{⇔}9x-\dfrac{35}{12}=0\\ \text{⇔}x=\dfrac{35}{108}\)
10.
\(-\dfrac{15}{2}+\dfrac{1}{4}+4x-2=1\\ \text{⇔}4x=\dfrac{41}{4}\\ \text{⇔}x=\dfrac{41}{16}\)
12.
\(\dfrac{2}{5}-\dfrac{1}{3}x+\dfrac{1}{6}=\dfrac{1}{4}\\ \text{⇔}\dfrac{17}{30}-\dfrac{1}{3}x=\dfrac{1}{3}\\ \text{⇔}\dfrac{1}{3}x=\dfrac{7}{30}\\ \text{⇔}x=\dfrac{7}{10}\)
14.
\(-1+\dfrac{2}{3}x=\dfrac{1}{8}-\dfrac{1}{6}\\ \text{⇔}\dfrac{2}{3}x=\dfrac{23}{24}\\ \text{⇔}x=\dfrac{23}{16}\)
5 tháng 9 2021
\(c,x\left(\dfrac{1}{5}+\dfrac{1}{4}\right)-\left(\dfrac{1}{7}+\dfrac{1}{8}\right)=0\\ \Leftrightarrow\dfrac{9}{20}x-\dfrac{15}{56}=0\\ \Leftrightarrow x=\dfrac{15}{56}\cdot\dfrac{20}{9}=\dfrac{25}{42}\)
\(d,\left(2x-\dfrac{2}{3}\right)\left(x+0,5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{2}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(4,\)
\(\left(-111\right):\left(-\dfrac{1}{11}\right)=1221\)
5 tháng 9 2021
d: Ta có: \(\left(2x-\dfrac{2}{3}\right)\left(x+\dfrac{1}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{2}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
giúp )):<
2) \(5^6\cdot5^4=5^{10}\)
5) \(3^7\cdot3^9=3^{16}\)
8) \(\left(-6\right)^5\cdot\left(-6\right)=\left(-6\right)^6=6^6\)
11) \(\left(\dfrac{4}{5}\right)^4\cdot\left(\dfrac{4}{5}\right)^3=\left(\dfrac{4}{5}\right)^7=\dfrac{16384}{78125}\)
14) \(\left(\dfrac{2}{3}\right)\cdot\left(\dfrac{2}{3}\right)^2=\left(\dfrac{2}{3}\right)^3=\dfrac{8}{27}\)