How do you solve $| - 2 x + 1 | < 1$ $|-2x+1|<1$ ?

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How do you solve $| - 2 x + 1 | < 1$ $|-2x+1|<1$ ?

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Answer 1 · 2018-03-03T13:58:56

$x > 0 and x < 1$ $x>0andx<1$

Explanation:

$| M + N | <$ $|M+N|<$ $K \Leftrightarrow$ $KhArr$ $M + N < (K) and$ $M+N<(K)and$ $M + N > (- K)$ $M+N>(-K)$
So,
$| - 2 x + 1 | < 1 \Leftrightarrow - 2 x + 1 < 1 and - 2 x + 1 > (- 1)$ $|-2x+1|<1hArr-2x+1<1and-2x+1>(-1)$
$\Leftrightarrow - 2 x < 1 - 1 and - 2 x > (- 1) - 1$ $hArr-2x<1-1and-2x>(-1)-1$
$\Leftrightarrow - 2 x < 0 and - 2 x > (- 2)$ $hArr-2x<0and-2x>(-2)$
Dividing both sides by (-2),
$\Leftrightarrow x > 0 and x < 1$ $hArrxcolor(red)(>)0andxcolor(red)(<)1$ (ineqalities change)

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How do you solve $| - 2 x + 1 | < 1$ $|-2x+1|<1$ ?

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