| 2-4x | = 4x-2

<=> \(\orbr{\begin{cases}\left|2-4x\right|=-2+4x=4x-2\\\left|2-4x\right|=2-4x=4x-2\end{cases}}\)

<=>\(\orbr{\begin{cases}-2+4x=4x-2\\2-4x=4x-2\end{cases}}\)

<=>\(\orbr{\begin{cases}-2+4x-4x+2=0\\2-4x-4x+2=0\end{cases}}\)

<=>\(\orbr{\begin{cases}0=0\\-8x+4=0\end{cases}}\)

<=> x=\(\frac{-4}{-8}=\frac{1}{2}\)

=> \(S=\left\{\frac{1}{2};\infty\right\}\)

2x-7> 3(x-1)

<=>2x-7>3x-3

<=>2x-3x>-3+7

<=>-x>4

<=>x<4

=>S={x/x<4}

1-2x<4(3x-2)

<=>1-2x<12x-8

<=>-2x-12x<-8-1

<=>-14x<-9

<=>x>\(\frac{9}{14}\)

=>S={\(\frac{9}{14}\)}

-3x+2|-4 -x|> 0

<=>\(\orbr{\begin{cases}-3x+2+4+x>0\\-3x+2-4x-x>0\end{cases}}\)

<=>\(\orbr{\begin{cases}-2x+6>0\\-8x+2>0\end{cases}}\)

<=>\(\orbr{\begin{cases}-2x>-6\\-8x>-2\end{cases}}\)

<=>\(\orbr{\begin{cases}x< 3\\x< \frac{1}{4}\end{cases}}\)

=>S={x/x<3;x/x<\(\frac{1}{4}\)}

4x-1|x-2|< 0

<=>\(\orbr{\begin{cases}4x-1-x+2< 0\\4x-1+x-2< 0\end{cases}}\)

<=>\(\orbr{\begin{cases}3x+1< 0\\3x-3< 0\end{cases}}\)

<=>\(\orbr{\begin{cases}3x< -1\\3x< 3\end{cases}}\)

<=>\(\orbr{\begin{cases}x< \frac{-1}{3}\\x< 1\end{cases}}\)

=>S={x/x<\(\frac{-1}{3}\);x/x<1}

c,x≤3/2

\(\dfrac{x+1}{\sqrt{2}+4}=\dfrac{\sqrt{3-2x}}{7}\)

ĐKXĐ: 3-2x>=0

=>2x<=3

=>x<=3/2

\(5\sqrt{x-1}-\sqrt{x+7}=3x-4\)

ĐK: \(\left\{{}\begin{matrix}x-1\ge0\\x+7\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\ge-7\end{matrix}\right.\Leftrightarrow x\ge1\)

\(pt\Leftrightarrow5\sqrt{x-1}=3x-4+\sqrt{x+7}\\ \Leftrightarrow25\left(x-1\right)=\left(3x-4\right)^2+2\left(3x-4\right)\sqrt{x+7}+x+7\\ \Leftrightarrow25x-25=9x^2-24x+16+\left(6x-8\right)\sqrt{x+7}+x+7\\ \Leftrightarrow9x^2-24x-25x+x+16+7+25=-\left(6x-8\right)\sqrt{x+7}\)

\(\Leftrightarrow9x^2-48x+48=\left(8-6x\right)\sqrt{x+7}\\ \Leftrightarrow\left(3x-8\right)^2-16=\left(8-6x\right)\sqrt{x+7}\\ \Leftrightarrow\left(3x-12\right)\left(3x-4\right)=-2\left(3x-4\right)\sqrt{x+7}\)

\(\Leftrightarrow3x-12=-2\sqrt{x+7}\\ \Leftrightarrow\left(3x-12\right)^2=4\left(x+7\right)\\ \Leftrightarrow9x^2-72x+144-4x-28=0\Leftrightarrow9x^2-76x+116=0\)

\(\Delta=\left(-76\right)^2-4.9.116=1600\)

\(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{76+\sqrt{1600}}{2.9}=\frac{58}{9}\left(TM\right)\\x_2=\frac{76-\sqrt{1600}}{2.9}=2\left(TM\right)\end{matrix}\right.\)

Hồng PhúcMiyuki MisakiNguyễn Lê Phước ThịnhMai.T.LoanTrần Đăng Nhất@Nguyễn Thành Trương@Nguyễn Việt Lâm

\(\sqrt{x}>2\Leftrightarrow x>4\)

\(5>\sqrt{x}\Leftrightarrow x< 25\)

\(\sqrt{x}< \sqrt{10}\Leftrightarrow x< 10\)( x không âm )

\(\sqrt{3x}< 3\Leftrightarrow3x< 9\Leftrightarrow x< 3\)

\(14\ge7\sqrt{2x}\Leftrightarrow\sqrt{2x}\le2\Leftrightarrow2x\le4\Leftrightarrow x\le2\)

Tham khảo nhé~

\(1.\sqrt{x}>2\left(Đk:x\ge0\right)\\ \Leftrightarrow\sqrt{x}>\sqrt{4}\)

\(\Leftrightarrow x>4\)