\(\left|3x-4\right|\le3\)
\(\Rightarrow\left\{{}\begin{matrix}3x-4\le3\\3x-4\ge-3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}3x\le7\\3x\le1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\le\dfrac{7}{3}\\x\ge\dfrac{1}{3}\end{matrix}\right.\) \(\Rightarrow\dfrac{1}{3}\le x\le\dfrac{7}{3}\)
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\(\left|3x-4\right|\le3\)
\(\left|3x-4\right|\ge0\)
\(\Leftrightarrow0\le\left|3x-4\right|\le3\)
\(\Leftrightarrow\left|3x-4\right|\in\left\{0;1;2;3\right\}\)
\(\Leftrightarrow3x-4=0\Rightarrow3x=4\Rightarrow x=\dfrac{4}{3}\)
\(\Leftrightarrow3x-4=1\Rightarrow3x=5\Rightarrow x=\dfrac{5}{3}\)
\(3x-4=-1\Rightarrow3x=3\Rightarrow x=1\)
\(\Leftrightarrow3x-4=2\Rightarrow3x=6\Rightarrow x=2\)
\(3x-4=-2\Rightarrow3x=2\Rightarrow x=\dfrac{2}{3}\)
\(\Leftrightarrow3x-4=3\Rightarrow3x=7\Rightarrow x=\dfrac{7}{3}\)
\(3x-4=-3\Rightarrow3x=1\Rightarrow x=\dfrac{1}{3}\)
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