Question

[LanAnh]

ghh

Answer 1

[YangSu]

\(a,\dfrac{7-3x}{12}+\dfrac{3}{4}=2\left(x-2\right)+\dfrac{5\left(5-2x\right)}{6}\\ \Leftrightarrow\dfrac{7-3x+9-12.2\left(x-2\right)-2.5\left(5-2x\right)}{12}=0\\ \Leftrightarrow7-3x+9-24x+48-50+20x=0\\ \Leftrightarrow-7x=-14\\ \Leftrightarrow x=2\)

\(b,\dfrac{1}{x-1}+\dfrac{2}{x^2+x+1}=\dfrac{3x^2}{x^3-1}\left(dk:x\ne1\right)\\ \Leftrightarrow\dfrac{x^2+x+1+2\left(x-1\right)-3x^2}{x^3-1}=0\\ \Leftrightarrow x^2+x+1+2x-2-3x^2=0\\ \Leftrightarrow-2x^2+3x-1=0\\ \Leftrightarrow-2x^2+2x+x-1=0\\ \Leftrightarrow-2x\left(x-1\right)+\left(x-1\right)=0\\ \Leftrightarrow\left(-2x+1\right)\left(x-1\right)=0\)

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

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

\(c,\dfrac{7x-2}{3}-2x< 5-\dfrac{x-2}{4}\\ \Leftrightarrow\dfrac{4\left(7x-2\right)-12.2x-5.12+3\left(x-2\right)}{12}< 0\\ \Leftrightarrow28x-8-24x-60+3x-6< 0\\ \Leftrightarrow7x< 74\\ \Leftrightarrow x=\dfrac{74}{7}\)

\(c,2x-x\left(3x+1\right)< 15-3x\left(x+2\right)\\ \Leftrightarrow2x-3x^2-x-15+3x^2+6x< 0\\ \Leftrightarrow7x< 15\\ \Leftrightarrow x< \dfrac{15}{7}\)

Answer 2

[LanAnh]

hv