a: \(\Leftrightarrow\dfrac{15-2x-1}{5}>\dfrac{x+3}{4}\)

\(\Leftrightarrow\dfrac{-8x+56}{20}>\dfrac{5x+15}{20}\)

=>-8x+56>5x+15

=>-11x>-41

hay x<41/11

b: \(\Leftrightarrow\dfrac{5x+5-6}{6}< \dfrac{4x+4}{6}\)

=>5x-1<4x+4

=>x<5

 \(3-\dfrac{2x+1}{5}>x+\dfrac{3}{4}.\)

\(\Leftrightarrow\dfrac{14-2x}{5}-x-\dfrac{3}{4}>0.\)

\(\Leftrightarrow\dfrac{56-8x-20x-15}{20}>0.\)

\(\Rightarrow-28x+41>0.\)

\(\Leftrightarrow-28x>-41.\)

\(\Leftrightarrow x< \dfrac{41}{28}.\)

d?

chọn nhiều đáp án

C nhé

Bài 1:

a. 

$(4x^2+4x+1)-x^2=0$

$\Leftrightarrow (2x+1)^2-x^2=0$

$\Leftrightarrow (2x+1-x)(2x+1+x)=0$

$\Leftrightarrow (x+1)(3x+1)=0$

$\Rightarrow x+1=0$ hoặc $3x+1=0$

$\Rightarrow x=-1$ hoặc $x=-\frac{1}{3}$

b.

$x^2-2x+1=4$

$\Leftrightarrow (x-1)^2=2^2$

$\Leftrightarrow (x-1)^2-2^2=0$

$\Leftrightarrow (x-1-2)(x-1+2)=0$

$\Leftrightarrow (x-3)(x+1)=0$

$\Leftrightarrow x-3=0$ hoặc $x+1=0$

$\Leftrightarrow x=3$ hoặc $x=-1$

c.

$x^2-5x+6=0$

$\Leftrightarrow (x^2-2x)-(3x-6)=0$

$\Leftrightarrow x(x-2)-3(x-2)=0$

$\Leftrightarrow (x-2)(x-3)=0$

$\Leftrightarrow x-2=0$ hoặc $x-3=0$

$\Leftrightarrow x=2$ hoặc $x=3$

2c.

ĐKXĐ: $x\neq 0$

PT $\Leftrightarrow x-\frac{6}{x}=x+\frac{3}{2}$

$\Leftrightarrow -\frac{6}{x}=\frac{3}{2}$

$\Leftrightarrow x=-4$ (tm)

2d.

ĐKXĐ: $x\neq 2$

PT $\Leftrightarrow \frac{1+3(x-2)}{x-2}=\frac{3-x}{x-2}$

$\Leftrightarrow \frac{3x-5}{x-2}=\frac{3-x}{x-2}$

$\Rightarrow 3x-5=3-x$

$\Leftrightarrow 4x=8$

$\Leftrightarrow x=2$ (không tm) 

Vậy pt vô nghiệm.

2f.

ĐKXĐ: $x\neq \pm 2$

PT $\Leftrightarrow \frac{(x-2)^2-3(x+2)}{(x+2)(x-2)}=\frac{2(x-11)}{(x-2)(x+2)}$

$\Rightarrow (x-2)^2-3(x+2)=2(x-11)$

$\Leftrightarrow x^2-4x+4-3x-6=2x-22$

$\Leftrightarrow x^2-7x-2=2x-22$

$\Leftrightarrow x^2-9x+20=0$

$\Leftrightarrow (x-4)(x-5)=0$

$\Leftrightarrow x-4=0$ hoặc $x-5=0$

$\Leftrightarrow x=4$ hoặc $x=5$ (tm)

a)

ĐKXĐ: \(x\notin\left\{3;-3\right\}\)

Ta có: \(\dfrac{2x}{x-3}=\dfrac{x^2+11x-6}{x^2-9}\)

\(\Leftrightarrow\dfrac{2x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2+11x-6}{\left(x-3\right)\left(x+3\right)}\)

Suy ra: \(2x^2+6x=x^2+11x-6\)

\(\Leftrightarrow2x^2+6x-x^2-11x+6=0\)

\(\Leftrightarrow x^2-5x+6=0\)

\(\Leftrightarrow x^2-2x-3x+6=0\)

\(\Leftrightarrow x\left(x-2\right)-3\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=3\left(loại\right)\end{matrix}\right.\)

Vậy: S={2}

b) Ta có: \(3x^2+\left(1-\sqrt{3}\right)x+\sqrt{3}-4=0\)

\(\Leftrightarrow3x^2-\left(\sqrt{3}-1\right)x+\sqrt{3}-4=0\)

\(\Leftrightarrow3x^2-\left(\sqrt{3}-1\right)x+\sqrt{3}-1-3=0\)

\(\Leftrightarrow\left(3x^2-3\right)-\left(\sqrt{3}-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-\left(\sqrt{3}-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(3x+3-\sqrt{3}+1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(3x+4-\sqrt{3}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x+4-\sqrt{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\3x=\sqrt{3}-4\end{matrix}\right.\)

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

Vậy: \(S=\left\{1;\dfrac{\sqrt{3}-4}{3}\right\}\)

a) Ta có: (5x-1)(x-3)<0

nên 5x-1 và x-3 trái dấu

Trường hợp 1:

\(\left\{{}\begin{matrix}5x-1>0\\x-3< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>\dfrac{1}{5}\\x< 3\end{matrix}\right.\Leftrightarrow\dfrac{1}{5}< x< 3\)

Trường hợp 2:

\(\left\{{}\begin{matrix}5x-1< 0\\x-3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< \dfrac{1}{5}\\x>3\end{matrix}\right.\Leftrightarrow loại\)

Vậy: S={x|\(\dfrac{1}{5}< x< 3\)}

a) \(2\chi-3=3\left(\chi+1\right)\)

\(\Leftrightarrow2\chi-3=3\chi+3\)

\(\Leftrightarrow2\chi-3\chi=3+3\)

\(\Leftrightarrow\chi=-6\)

Vậy phương trình có tập nghiệm S= \(\left\{-6\right\}\)

\(3\chi-3=2\left(\chi+1\right)\)

\(\Leftrightarrow3\chi-3=2\chi+2\)

\(\Leftrightarrow3\chi-2\chi=2+3\)

\(\Leftrightarrow\chi=5\)

Vậy phương trình có tập nghiệm S= \(\left\{5\right\}\)

b) \(\left(3\chi+2\right)\left(4\chi-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3\chi+2=0\\4\chi-5=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3\chi=-2\\4\chi=5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\chi=\dfrac{-2}{3}\\\chi=\dfrac{5}{4}\end{matrix}\right.\)

Vậy phương trình có tập nghiệm S= \(\left\{\dfrac{-2}{3};\dfrac{5}{4}\right\}\)

\(\left(3\chi+5\right)\left(4\chi-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3\chi+5=0\\4\chi-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3\chi=-5\\4\chi=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\chi=\dfrac{-5}{3}\\\chi=\dfrac{1}{2}\end{matrix}\right.\)

Vậy phương trình có tập nghiệm S= \(\left\{\dfrac{-5}{3};\dfrac{1}{2}\right\}\)

c) \(\left|\chi-7\right|=2\chi+3\)

Trường hợp 1: 

Nếu \(\chi-7\ge0\Leftrightarrow\chi\ge7\)

Khi đó:\(\left|\chi-7\right|=2\chi+3\)

 \(\Leftrightarrow\chi-7=2\chi+3\)

\(\Leftrightarrow\chi-2\chi=3+7\)

\(\Leftrightarrow\chi=-10\) (KTMĐK)

Trường hợp 2:

Nếu \(\chi-7\le0\Leftrightarrow\chi\le7\)

Khi đó: \(\left|\chi-7\right|=2\chi+3\)

\(\Leftrightarrow-\chi+7=2\chi+3\)

\(\Leftrightarrow-\chi-2\chi=3-7\)

\(\Leftrightarrow-3\chi=-4\)

\(\Leftrightarrow\chi=\dfrac{4}{3}\)(TMĐK)

Vậy phương trình có tập nghiệm S=\(\left\{\dfrac{4}{3}\right\}\)

\(\left|\chi-4\right|=5-3\chi\)

Trường hợp 1:  

Nếu \(\chi-4\ge0\Leftrightarrow\chi\ge4\)

Khi đó: \(\left|\chi-4\right|=5-3\chi\)

\(\Leftrightarrow\chi-4=5-3\chi\)

\(\Leftrightarrow\chi+3\chi=5+4\)

\(\Leftrightarrow4\chi=9\)

\(\Leftrightarrow\chi=\dfrac{9}{4}\)(KTMĐK)

Trường hợp 2: Nếu \(\chi-4\le0\Leftrightarrow\chi\le4\)

Khi đó: \(\left|\chi-4\right|=5-3\chi\)

\(\Leftrightarrow-\chi+4=5-3\chi\)

\(\Leftrightarrow-\chi+3\chi=5-4\)

\(\Leftrightarrow2\chi=1\)

\(\Leftrightarrow\chi=\dfrac{1}{2}\)(TMĐK)

Vậy phương trình có tập nghiệm S=\(\left\{\dfrac{1}{2}\right\}\)

a: \(2^{2x-2}>=8\)

=>\(2^{2x-2}>=2^3\)

=>2x-2>=3

=>2x>=5

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

b: \(4^{2x+2}< =16\)

=>\(4^{2x+2}< =4^2\)

=>2x+2<=2

=>2x<=0

=>x<=0

c: \(5^{x-9}>5^2\)

=>x-9>2

=>x>11

d: \(9^{x+2}< 9\)

=>\(9^{x+2}< 9^1\)

=>x+2<1

=>x<-1

e: \(9^{x-1}>9^{x^2-x-9}\)

=>\(x-1>x^2-x-9\)

=>\(x^2-x-9-x+1< 0\)

=>\(x^2-2x-8< 0\)

=>(x-4)(x+2)<0

=>-2<x<4

a) \(\left(x-2\right)^2=\left(x-4\right)\left(x+4\right)\) 

\(\Leftrightarrow x^2-4x+4-x^2+16=0\)

\(\Leftrightarrow20-4x=0\)

\(\Leftrightarrow4x=20\)

\(\Leftrightarrow x=5\)

Vậy S = {5}

b) ĐKXĐ: \(x\ne0;x\ne-2\)

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

\(\Leftrightarrow\dfrac{x+2}{x}=\dfrac{x^2+4x+x+4+x^2}{x\left(x+2\right)}\)

\(\Leftrightarrow\dfrac{x+2}{x}=\dfrac{2x^2+5x+4}{x\left(x+2\right)}\)

\(\Rightarrow x\left(x+2\right)^2=x\left(2x^2+5x+4\right)\)

\(\Leftrightarrow x^3+4x^2+4x=2x^3+5x^2+4x\)

\(\Leftrightarrow x^3+x^2=0\)

\(\Leftrightarrow x^2\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-1\left(TM\right)\end{matrix}\right.\)

Vậy S = {-1}

c) Câu này mình không chắc về đề lắm! Bạn dùng ô chữ M bị ngược để viết lại đề nhé!

a) Ta có: \(\left(x-2\right)^2=\left(x-4\right)\left(x+4\right)\)

\(\Leftrightarrow x^2-4x+4=x^2-16\)

\(\Leftrightarrow x^2-4x+4-x^2+16=0\)

\(\Leftrightarrow-4x+20=0\)

\(\Leftrightarrow-4x=-20\)

hay x=5

Vậy: S={5}