Question

a, | x - 1/2| ≤ 1/3

b, | 2x - 1/2 | > | - 1,5 |

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Answer 1

a) \(\left|x-\dfrac{1}{2}\right|\le\dfrac{1}{3}\)

\(\Leftrightarrow-\dfrac{1}{3}\le x-\dfrac{1}{2}\le\dfrac{1}{3}\)

\(\Leftrightarrow\dfrac{1}{6}\le x\le\dfrac{5}{6}\)

b) \(\left|2x-\dfrac{1}{2}\right|>\left|-1,5\right|\)

\(\Leftrightarrow\left|2x-\dfrac{1}{2}\right|>\dfrac{3}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{1}{2}>\dfrac{3}{2}\\2x-\dfrac{1}{2}< \dfrac{3}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x>2\\2x< 1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>1\\x< \dfrac{1}{2}\end{matrix}\right.\)