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Xét \(5-x=0\Leftrightarrow x=5\)
\(x-1=0\Leftrightarrow x=1\)
\(2+3x=0\Leftrightarrow x=-\dfrac{2}{3}\)
Bảng xét dấu:
Để VT\(\le\)0 <=>\(\left[{}\begin{matrix}-\dfrac{2}{3}\le x\le1\\x\ge5\end{matrix}\right.\)
Vậy...
\(2+\dfrac{3\left(x+1\right)}{3}\le3-\dfrac{x-1}{4}\)
\(\Leftrightarrow2+x+1\le\dfrac{12}{4}-\dfrac{x-1}{4}\)
\(\Leftrightarrow x+3\le\dfrac{13-x}{4}\)
\(\Leftrightarrow\dfrac{4x+12}{4}\le\dfrac{13-x}{4}\)
\(\Leftrightarrow4x+12\le13-x\)
\(\Leftrightarrow4x+x\le13-12\)
\(\Leftrightarrow5x\le1\)
\(\Leftrightarrow x\le\dfrac{1}{5}\)
Vậy: \(x\le\dfrac{1}{5}\)
\(2+\dfrac{3\left(x+1\right)}{3}\le3-\dfrac{x-1}{4}\)
\(\Leftrightarrow\dfrac{12x+36}{12}\le\dfrac{33-3x}{12}\)
\(\Leftrightarrow12x+36\le33-3x\)
\(\Leftrightarrow12x+3x\le-36+33\)
\(\Leftrightarrow15x\le-3\)
\(\Leftrightarrow x\le\dfrac{-1}{5}\)
\(a,\dfrac{2x-1}{3}< \dfrac{x+6}{2}\)
\(\Leftrightarrow\dfrac{4x-2}{6}< \dfrac{3x+18}{6}\)
\(\Leftrightarrow4x-2< 3x+18\)
\(\Leftrightarrow4x-3x< 2+18\)
\(\Leftrightarrow x< 20\)
\(b,\dfrac{5\left(x-1\right)}{6}-1>\dfrac{2\left(x+1\right)}{3}\)
\(\Leftrightarrow\dfrac{5x-11}{6}>\dfrac{4x+4}{6}\)
\(\Leftrightarrow5x-11>4x+4\)
\(\Leftrightarrow5x-4x>11+4\)
\(\Leftrightarrow x>15\)
\(x-4\)
\(\left(\sqrt{2}\right)^2-4\)
\(=\left(\sqrt{2}-2\right)\left(\sqrt{2}+2\right)\)
\(x^2-5x+6\le0\)
\(\Leftrightarrow x^2-2x-3x+6\le0\)
\(\Leftrightarrow x.\left(x-2\right)-3.\left(x-2\right)\le0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)\le0\)
\(\text{Mà }x-2>x-3\text{ nên :}\)
\(x-2\ge0\text{ và }x-3\le0\)
\(\Leftrightarrow x\ge2\text{ và }x\le3\Rightarrow2\le x\le3\)