`Answer:`

c) \(\frac{2\left(3x+5\right)}{3}-\frac{x}{x}=5-\frac{3\left(x+1\right)}{4}\)

\(\Leftrightarrow\frac{8\left(3x+5\right)}{12}-\frac{6x}{12}=\frac{60}{12}-\frac{9\left(x+1\right)}{12}\)

\(\Rightarrow24x+40-6x=60-9x-9\)

\(\Leftrightarrow24x+9x-6x=60-9-40\)

\(\Leftrightarrow27x=11\)

\(\Leftrightarrow x=\frac{11}{27}\)

d) \(x^2-4x+4\)

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

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

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

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

e) \(\frac{x-1}{x+2}-\frac{x}{x-2}=\frac{5x-8}{x^2-4}\left(ĐKXĐ:x\ne\pm2\right)\)

\(\Leftrightarrow\frac{x-2}{x+2}-\frac{x}{x-2}=\frac{5x-8}{\left(x+2\right)\left(x-2\right)}\)

\(\Leftrightarrow\frac{\left(x-1\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{5x-8}{\left(x+2\right)\left(x-2\right)}\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)-x\left(x+2\right)=5x-8\)

\(\Leftrightarrow x^2-2x-x+2-x^2-2x=5x-8\)

\(\Leftrightarrow-5x+2=5x-8\)

\(\Leftrightarrow-10x=-10\)

\(\Leftrightarrow x=1\)

\(a^4+b^4\ge ab^3+ba^3\)

\(\Leftrightarrow a^4+b^4-ab^3-ba^3\ge0\)

\(\Leftrightarrow\left(a-b\right)^2\left(a^2+ab+b^2\right)\ge0\)(đúng)

Vậy ta có điều phải chứng minh.

`Answer:`

\(4x-\frac{2x-1}{4}\le\frac{3x-2}{6}\)

\(\Leftrightarrow\frac{16x-2x+1}{4}\le\frac{3x-2}{6}\)

\(\Leftrightarrow\frac{14x+1}{4}\le\frac{3x-2}{6}\)

\(\Leftrightarrow3.\left(14x+1\right)\le2.\left(3x-2\right)\)

\(\Leftrightarrow42x+3\le6x-4\)

\(\Leftrightarrow42x-6x\le-4-3\)

\(\Leftrightarrow36x\le-7\)

\(\Leftrightarrow x\le-\frac{7}{36}\)

\(4x\left(3x-2\right)=4-6x\)\(\Leftrightarrow4x\left(3x-2\right)+6x-4=0\)\(\Leftrightarrow4x\left(3x-2\right)+2\left(3x-2\right)=0\)\(\Leftrightarrow2\left(3x-2\right)\left(2x+1\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}3x-2=0\\2x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-\frac{1}{2}\end{cases}}\)

Vậy tập nghiệm của pt đã cho là \(S=\left\{-\frac{1}{2};\frac{2}{3}\right\}\)

`Answer:`

9B.

a. \(\frac{x+81}{19}+\frac{x+82}{18}>\frac{x+84}{16}+\frac{x+85}{15}\)

\(\Leftrightarrow\frac{x+81}{19}+1+\frac{x+82}{18}+1>\frac{x+84}{16}+1+\frac{x+85}{15}+1\)

\(\Leftrightarrow\frac{x+81+19}{19}+1+\frac{x+82+18}{18}+1>\frac{x+84+16}{16}+1+\frac{x+85+15}{15}+1\)

\(\Leftrightarrow\frac{x+100}{19}+\frac{x+100}{18}-\frac{x+100}{16}-\frac{x+100}{15}>0\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{19}+\frac{1}{18}-\frac{1}{16}-\frac{1}{15}\right)>0\)

Mà \(\frac{1}{19}+\frac{1}{18}-\frac{1}{16}-\frac{1}{15}< 0\)

\(\Rightarrow x+100< 0\Leftrightarrow x< -100\)

b. \(\frac{x-22}{8}+\frac{x-21}{9}+\frac{x-20}{10}+\frac{x-19}{11}< 4\)

\(\Leftrightarrow\left(\frac{x-22}{8}-1\right)+\left(\frac{x-21}{9}-1\right)+\left(\frac{x-20}{10}-1\right)+\left(\frac{x-19}{11}-1\right)< 4-1-1-1-1\)

\(\Leftrightarrow\frac{x-22-8}{8}+\frac{x-21-9}{9}+\frac{x-20-10}{10}+\frac{x-19-11}{11}< 0\)

\(\Leftrightarrow\frac{x-30}{8}+\frac{x-30}{9}+\frac{x-30}{10}+\frac{x-30}{11}< 0\)

\(\Leftrightarrow\left(x-30\right)\left(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)< 0\)

Mà \(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}>0\)

\(\Rightarrow x-30< 0\Leftrightarrow x< 30\)

\(a>b\Leftrightarrow-6a< -6b\Leftrightarrow-6a+1< -6b+1\)

Bạn thử làm ngược lại xem ?!

`Answer:`

\(\left|2x-4\right|-5x=12\)

\(\Rightarrow\left|2x-4\right|=5x+12\)

Ta có:

\(\left|2x-4\right|=2x-4\Leftrightarrow2x-4\ge0\) hay \(x\ge2\)

\(\left|2x-4\right|=-2x+4\Leftrightarrow2x-4< 0\) hay \(x< 2\)

Với `x>=2:`

\(2x-4=5x+12\)

\(\Leftrightarrow2x-5x=4+12\)

\(\Leftrightarrow-3x=16\)

\(\Leftrightarrow x=-\frac{16}{3}\text{(Loại)}\)

Với `x<2:`

\(-2x+4=5x+12\)

\(\Leftrightarrow-2x-5x=-4+12\)

\(\Leftrightarrow-7x=8\)

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

là hinh học hay là linh tinh vậy bn?

Là sao vậy ạ, nhìn chả hiều gì cả.