\(\frac{x-1}{3}\cdot\frac{x+2}{5}>0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)>0\)

\(TH1:\orbr{\begin{cases}x-1>0\\x+2>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x>1\\x>-2\end{cases}}\Leftrightarrow x>1\left(1\right)\)

\(TH2:\orbr{\begin{cases}x-1< 0\\x+2< 0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< 1\\x< -2\end{cases}}\Leftrightarrow x< -2\left(2\right)\)

Tu ( 1 ) va ( 2 ) suy ra \(-2< x< 1\)

Cho mik sua 1 chut nha.

\(TH1:\Leftrightarrow x>-2\)

\(TH2:\Leftrightarrow x< 1\)

\(\left(x-\frac{1}{3}\right)\left(x+\frac{2}{5}\right)>0\)

\(\orbr{\begin{cases}x=\frac{1}{3}\\x=-\frac{2}{5}\end{cases}}\)

\(-\frac{2}{5}< x< \frac{1}{3}\)

\(\frac{2}{3}-\frac{1}{3}.\frac{x-3}{2}-\frac{1}{2}.2.x+1=5\)

\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{3.2}-\frac{2.x}{2}+1=5\)

\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{6}-x+1=5\)

\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{6}-x=4\)

\(\Leftrightarrow\frac{4}{6}-\frac{x-3}{6}-\frac{6x}{6}=4\)

\(\Leftrightarrow\frac{4-\left(x-3\right)-6x}{6}=4\)

\(\Leftrightarrow\frac{4-x+3+6x}{6}=4\)

\(\Leftrightarrow\frac{4+3-x+6x}{6}=\frac{4}{1}\)

\(\Leftrightarrow\frac{7+5x}{6}=\frac{4}{1}\)

\(\Leftrightarrow7+5x=4.6\)

\(\Leftrightarrow7+5x=24\)

\(\Leftrightarrow5x=24-7\)

\(\Leftrightarrow5x=17\)

\(\Leftrightarrow x=\frac{17}{5}\)

Vậy \(x=\frac{17}{5}\)

Chúc bạn học tốt

(\(x\) + \(\dfrac{1}{2}\))² = \(\dfrac{1}{16}\)

\(\left[{}\begin{matrix}x+\dfrac{1}{2}=-\dfrac{1}{4}\\x+\dfrac{1}{2}=\dfrac{1}{4}\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=-\dfrac{1}{4}-\dfrac{1}{2}\\x=\dfrac{1}{4}-\dfrac{1}{2}\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

Vậy \(x\) \(\in\) {- \(\dfrac{3}{4};-\dfrac{1}{4}\)}

\(x\) : (- \(\dfrac{1}{3}\))³  = - \(\dfrac{1}{3}\)

\(x\)              = (-\(\dfrac{1}{3}\)).(-\(\dfrac{1}{3}\))³

\(x\)             = \(\dfrac{1}{81}\)

Vậy \(x=\dfrac{1}{81}\)

(\(\dfrac{2}{3}\))⁵\(x\) = \(\dfrac{2}{5}\)

       \(x\) = \(\dfrac{2}{5}\) : (\(\dfrac{2}{3}\))⁵ 

       \(x\) = \(\dfrac{243}{80}\)

Vậy \(x\) = \(\dfrac{243}{80}\)

\(\left(x-\frac{1}{2}\right)^2=0\)

\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=0^2\)

\(\Leftrightarrow x-\frac{1}{2}=0\)

\(\Leftrightarrow x=\frac{1}{2}\)

Vậy x = 1/2

\(\left(x-2\right)^2=1\)

\(\Leftrightarrow\left(x-2\right)^2=1^2\)

\(\Leftrightarrow x-2=1\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}}\)

Vậy x = 3 hoặc x = 1

\(\left(2x-1\right)^3=-8\)

\(\Leftrightarrow\left(2x-1\right)^3=\left(-2\right)^3\)

\(\Leftrightarrow2x-1=-2\)

<=> 2x = -1

<=> x = -0,5

Vậy x = -0,5

\(\left(x-\frac{1}{2}\right)^2=0\)

\(x-\frac{1}{2}=0\)

\(x=\frac{1}{2}\)

\(\left(x-2\right)^2=1\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1+2\\x=-1+2\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

Vậy\(x\in\left\{3;1\right\}\)
\(\left(2x-1\right)^3=-8\)

\(\left(2x-1\right)^3=\left(-2\right)^3\)

\(2x-1=-2\)

\(2x=\left(-2\right)+1\)

\(2x=-1\)

\(x=-1\times2\)

\(x=-2\)

\(x\left(\frac{1}{2}\right)^2=\frac{1}{16}\)

\(x\left(\frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x\frac{1}{2}=\frac{1}{4}\\x\frac{1}{2}=-\frac{1}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{4}:\frac{1}{2}\\x=-\frac{1}{4}:\frac{1}{2}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{2}\end{cases}}}\)

\(49\times7^x=2401\)

   \(7^x=2401:49\)

\(7^x=49\)

\(7^x=7^2\)

\(\Rightarrow x=2\)

\(2x^x-15=17\)

\(2x^x=17+15\)

\(2x^x=32\)

\(2x^x=2^5\)

\(\Rightarrow x\times x=5\)

\(\Rightarrow x^2=5\)

\(2^x+3\times2^x=32\)

\(2^x\times\left(3+1\right)=32\)

\(2^x\times4=32\)

\(2^x=32:4\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

\(2x\left(x-\frac{1}{7}\right)=0\)

\(x\left(x-\frac{1}{7}\right)=0:2\)

\(x\left(x-\frac{1}{7}\right)=0\)

\(x\times x-x\times\frac{1}{7}=0\)

\(x^2-x\frac{1}{7}=0\)

\(x-x=0:\frac{1}{7}\)

\(x-x=0\)

\(\Rightarrow x=0\)

\(\left(\frac{3}{4}x-\frac{9}{16}\right)-\left(\frac{1}{3}+\frac{-3}{5}x\right)=0.\)

\(\frac{3}{4}x-\frac{9}{16}-\frac{1}{3}-\frac{-3}{5}x=0\)

\(\frac{27}{20}x-\frac{43}{48}=0\)

\(\frac{27}{20}x=\frac{43}{48}\)

\(x=\frac{215}{324}\)

mong ủng hộ mk 

(3 phần 4 nhân X - 9 phần 16 ) - (1 phần 3 + -3 phần 5 chia X ) = 0

=>\(\frac{3}{4}.x-\frac{9}{16}=\frac{1}{3}+\frac{-3}{5}:x\)

=\(\frac{3}{4}.x-\frac{9}{16}=\frac{-4}{15}:x\)

=>\(\frac{3}{4}.x-\frac{-4}{15}:x=\frac{9}{16}\)

Đến đây thì mk chịu =)

Dù sao thi cg ti.ck giúp mk tí

a) x.(x-1) - 2(1-x) =0

=> x.(x-1) + 2(x-1) =0

=> (x-1)(x+2) =0

b) (x-3)^3 + (3-x) =0

=> (x-3)^3 - (x-3) =0

=> (x-3)​​[(x-3)^2 - 1 ] =0

=> (x-3)(x-3-1)(x-3+1) =0

=> (x-3)(x-4)(x-2) =0

12 phần 25 trừ cho 14 phần 5 bằng bao nhiêu

8==D LOL