Giúp mình hoàn thành các bài tập này với ạ.Cảm ơn rất nhìuuuuuuu @@@

@Akai Haruma

a/ \(\frac{x}{2}+\frac{18}{x}\ge2\sqrt{\frac{x}{2}.\frac{18}{x}}=...\)

b/ \(\frac{x}{2}+\frac{2}{x-1}=\frac{x-1}{2}+\frac{2}{x-1}+\frac{1}{2}\ge2\sqrt{\frac{x-1}{2}.\frac{2}{x-1}}+\frac{1}{2}=...\)

c/ \(\frac{3x}{2}+\frac{1}{x+1}=\frac{3\left(x+1\right)}{2}+\frac{1}{x+1}-\frac{3}{2}\ge2\sqrt{\frac{3\left(x+1\right)}{2}.\frac{1}{x+1}}-\frac{3}{2}=...\)

d/ \(\frac{x}{3}+\frac{5}{2x-1}=\frac{2x-1}{6}+\frac{5}{2x-1}+\frac{1}{6}\ge2\sqrt{\frac{2x-1}{6}.\frac{5}{2x-1}}+\frac{1}{6}=...\)

e/ \(\frac{x}{1-x}+\frac{5}{x}=\frac{x}{1-x}+\frac{5-5x+5x}{x}=\frac{x}{1-x}+\frac{5\left(1-x\right)}{x}+5\ge2\sqrt{\frac{x}{1-x}.\frac{5\left(1-x\right)}{x}}+5=...\)

f/ \(\frac{x^3+1}{x^2}=x+\frac{1}{x^2}=\frac{x}{2}+\frac{x}{2}+\frac{1}{x^2}\ge2\sqrt{\frac{x}{2}.\frac{x}{2}.\frac{1}{x^2}}=...\)

g/ \(\frac{x^2+4x+4}{x}=x+\frac{4}{x}+4\ge2\sqrt{x.\frac{4}{x}}+4=...\)

\(\frac{3x-7}{5}=\frac{2x-1}{3}\)

\(\Leftrightarrow9x-21=10x-5\)

\(\Leftrightarrow-x=16\Leftrightarrow x=-16\)

\(\frac{4x-7}{12}-x=\frac{3x}{8}\)

\(\Leftrightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow-56-64x=36x\)

\(\Leftrightarrow-56=100x\Leftrightarrow x=\frac{-14}{25}\)

\(\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\)

\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)=0\)

Vì \(\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)\ne0\)nên x - 2019 = 0

Vậy x = 2019

\(\frac{5x-8}{3}=\frac{1-3x}{2}\)

\(\Leftrightarrow10x-16=3-9x\)

\(\Leftrightarrow19x=19\Leftrightarrow x=1\)

\(\frac{x-5}{6}-\frac{x-9}{4}=\frac{5x-3}{8}+2\)

\(\Rightarrow\frac{4x-20-6x+54}{24}=\frac{5x-3+16}{8}\)

\(\Rightarrow\frac{-2x+34}{24}=\frac{5x+13}{8}\)

\(\Rightarrow-16x-272=120x+312\)

\(\Leftrightarrow-136x=584\Leftrightarrow x=\frac{-73}{17}\)

d: =>4x+6=15x-12

=>4x-15x=-12-6=-18

=>-11x=-18

hay x=18/11

e: =>\(45x+27=12+24x\)

=>21x=-15

hay x=-5/7

f: =>35x-5=96-6x

=>41x=101

hay x=101/41

g: =>3(x-3)=90-5(1-2x)

=>3x-9=90-5+10x

=>3x-9=10x+85

=>-7x=94

hay x=-94/7

a,ĐKXĐ \(x\ne-1;-\frac{1}{2}\)

Ta thấy x=0 không là nghiệm của PT

Xét \(x\ne0\)

Khi đó PT 

<=> \(\frac{2}{6x-1+\frac{3}{x}}+\frac{5}{4x+5+\frac{2}{x}}+\frac{1}{2x+3+\frac{1}{x}}=\frac{1}{3}\)

Đặt \(2x+\frac{1}{x}=a\)

=> \(\frac{2}{3a-1}+\frac{5}{2a+5}+\frac{1}{a+3}=\frac{1}{3}\)

<=>  \(3\left(25a^2+75a+10\right)=6a^3+31a^2+34a-15\)

<=> \(6a^3-44a^2-191a-45=0\)

Xin lỗi đến đây tớ ra nghiệm không đẹp 

c, \(x^2+\frac{9x^2}{\left(x+3\right)^2}=7\)   ĐKXĐ \(x\ne-3\)

<=> \(\left(x-\frac{3x}{x+3}\right)^2+2.\frac{3x^2}{x+3}=7\)

<=> \(\left(\frac{x^2}{x+3}\right)^2+6.\frac{x^2}{x+3}-7=0\)

<=> \(\left(\frac{x^2}{x+3}+7\right)\left(\frac{x^2}{x+3}-1\right)=0\)

<=> \(\orbr{\begin{cases}x^2+7x+21=0\\x^2-x-3=0\end{cases}}\)

\(S=\left\{\frac{1\pm\sqrt{13}}{2}\right\}\)thỏa mãn ĐKXĐ

b,\(\frac{1}{x+1}+\frac{2}{x+2}+\frac{1}{x+3}=\frac{1}{x+4}+\frac{2}{x+5}+\frac{1}{x+6}\)ĐKXĐ \(x\ne-1;-2;-3;-4;-5;-6\)

<=>\(\left(\frac{1}{x+1}-\frac{1}{x+6}\right)+2\left(\frac{1}{x+2}-\frac{1}{x+5}\right)+\left(\frac{1}{x+3}-\frac{1}{x+4}\right)=0\)

<=>\(\frac{5}{x^2+7x+6}+\frac{6}{x^2+7x+10}+\frac{1}{x^2+7x+12}=0\)

Đặt \(x^2+7x+6=a\)

=> \(\frac{5}{a}+\frac{6}{a+4}+\frac{1}{a+6}=0\)

<=> \(12a^2+90a+120=0\)

<=> \(a=\frac{-15\pm\sqrt{65}}{4}\)

Thay vào tính x nhưng bài này tớ ra nghiệm không đẹp

Vì số lượng bài khá nhiều và mình cũng không có quá nhiều thời gian nên không tránh khỏi sai sót, nếu phát hiện mong bạn thông cảm! Bài của tớ làm khá tắt bước, chỉ nên tham khảo. Bạn có thể tự biểu diễn tập nghiệm được không?

a. \(x+8>3x-1\)

\(\Leftrightarrow-2x>-9\)

\(\Leftrightarrow x< \frac{9}{2}\)

b. \(3x-\left(2x+5\right)\le\left(2x-3\right)\)

\(\Leftrightarrow3x-2x-5\le2x-3\)

\(\Leftrightarrow-x\le2\)

\(\Leftrightarrow x\ge2\)

c. \(\left(x-3\right)\left(x+3\right)< x\left(x+2\right)+3\)

\(\Leftrightarrow x^2-9< x^2+2x+3\)

\(\Leftrightarrow2x>-12\Leftrightarrow x>-6\)

d. \(2\left(3x-1\right)-2x< 2x+1\)

\(\Leftrightarrow6x-2-2x< 2x+1\)

\(\Leftrightarrow2x< 3\)

\(\Leftrightarrow x< \frac{3}{2}\)

e. \(\frac{3-2x}{5}>\frac{2-x}{3}\)

\(\Leftrightarrow3\left(3-2x\right)>5\left(2-x\right)\)

\(\Leftrightarrow9-6x>10-5x\)

\(\Leftrightarrow-x>1\) \(\Leftrightarrow x< -1\)

f. \(\frac{x-2}{6}-\frac{x-1}{3}\le\frac{x}{2}\)

\(\Leftrightarrow x-2-2\left(x-1\right)\le3x\)

\(\Leftrightarrow x-2-2x+2\le3x\)

\(\Leftrightarrow-4x\le0\Leftrightarrow x\ge0\)

g. \(\frac{x+1}{3}>\frac{2x-1}{6}\ge4\)

\(\Leftrightarrow2x+2>2x-1\ge24\)

\(\Leftrightarrow2x+2>2x\ge25\)

\(\Leftrightarrow x\ge\frac{25}{2}\)

h. \(1+\frac{2x+1}{3}>\frac{2x-1}{6}-2\)

\(\Leftrightarrow6+4x+2>2x-1-12\)

\(\Leftrightarrow2x>-25\)

\(\Leftrightarrow x>-\frac{25}{2}\)

i. \(\frac{x+5}{6}-\frac{2x+1}{3}\le\frac{x+3}{2}\)

\(\Leftrightarrow x+5-4x-2\le3x+9\)

\(\Leftrightarrow-6x\le6\)

\(\Leftrightarrow x\ge-1\)

j. \(\frac{5x+4}{6}-\frac{2x-1}{12}\ge4\)

\(\Leftrightarrow10x+8-2x+1\ge48\)

\(\Leftrightarrow8x\ge39\)

\(\Leftrightarrow x\ge\frac{39}{8}\)

Bạn tự biểu diễn nghiệm trên trục số nhé!

a) \(x+8>3x-1\)

\(\Leftrightarrow x-3x>-8-1\)

\(\Leftrightarrow-2x>-9\)

\(\Leftrightarrow x< \frac{9}{2}\)

b)

d)

e) \(\frac{3-2x}{5}>\frac{2-x}{3}\)

\(\Leftrightarrow\frac{\left(3-2x\right)\times3}{15}>\frac{\left(2-x\right)\times5}{15}\)

\(\Leftrightarrow9-6x>10-5x\)

\(\Leftrightarrow-6x+5x>-9+10\)

\(\Leftrightarrow-x>1\)

\(\Leftrightarrow x< -1\)

f)\(\frac{x-2}{6}-\frac{x-1}{3}\le\frac{x}{2}\)

\(\Leftrightarrow x-2-2\left(x-1\right)\le3x\)

\(\Leftrightarrow x-2-2x+2\le3x\)

\(\Leftrightarrow-4x\le0\)

\(\Leftrightarrow x\ge0\)

g) \(\frac{x+1}{3}>\frac{2x-1}{6}\ge4\)

\(\Leftrightarrow\frac{\left(x+1\right)\cdot2}{6}>\frac{2x-1}{6}\ge\frac{4\cdot6}{6}\)

\(\Leftrightarrow2x+2>2x+1\ge24\)

\(\Leftrightarrow2x+2>2x\ge25\)

\(\Leftrightarrow x\ge\frac{25}{2}\)

h)\(1+\frac{2x+1}{3}>\frac{2x-1}{6}-2\)

\(\Leftrightarrow\frac{1}{6}+\frac{\left(2x+1\right)\cdot2}{6}>\frac{2x-1}{6}-\frac{2\cdot6}{6}\)

\(\Leftrightarrow6+4x+2>2x-1-12\)

\(\Leftrightarrow2x>-21\)

\(\Leftrightarrow x>\frac{-21}{2}\)

i)\(\frac{x+5}{6}-\frac{2x+1}{3}\le\frac{x+3}{2}\)

\(\Leftrightarrow\frac{x+5}{6}-\frac{\left(2x+1\right)\cdot2}{6}\le\frac{\left(x+3\right)\cdot3}{6}\)

\(\Leftrightarrow x+5-4x+2\le3x+9\)

\(\Leftrightarrow-3x-x+4x\le9-5-2\)

\(\Leftrightarrow x\le2\)

j) \(\frac{5x+4}{6}-\frac{2x-1}{12}\ge4\)

\(\Leftrightarrow\frac{\left(5x+4\right)\cdot2}{12}-\frac{2x-1}{12}\ge\frac{4\cdot12}{12}\)

\(\Leftrightarrow10x+8-2x-1\ge48\)

\(\Leftrightarrow10x-2x\ge48-8+1\)

\(\Leftrightarrow8x\ge41\)

\(\Leftrightarrow x\ge\frac{41}{8}\)

Mình không chắc là mình làm đúng đâu. Nhưng có sai sót gì thì cứ nói cho mình biết. Chúc bạn học tốt ^-^

a, »x – 3x > -1 – 8

»-2x > -9

» x < \(\frac{9}{2}\)

b, » 3x – 2x – 5 ≤ 2x – 3

» 3x – 2x – 2x ≤ -3+5

» -x ≤ 2

» x ≥ -2

c, » x² + 3 x - 3 x - 9 < x² + 2x + 3

» x² + 3 x – 3 x – x² -2 x < 3 + 9

» -2x < 12

» x > -6

d, » 6 x -2 - 2 x < 2x + 1

» 6 x – 2 x – 2 x < 1+2

» 2x < 3

» x < \(\frac{3}{2}\)