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বাস্তব সংখ্যায় $\left|3x+2\right|<7$ অসমতাটির সমাধান কী?

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বাস্তব সংখ্যায় $\left|3x+2\right|<7$ অসমতাটির সমাধান কী?

Options :

  • (ক) $-3 < x <3$
  • (খ) $-\frac53 < x < \frac53$
  • (গ) $-3 < x < \frac53$
  • (ঘ) $\frac53 < x < -\frac53$

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$\left|3x\;+\;2\right|<7$

$\Rightarrow-7<3x+2<7$

$\Rightarrow-7-2<3x+2-2<7-2$

$\Rightarrow-9<3x<5$

$\Rightarrow-\frac93<\frac{3x}3<\frac53$

$\therefore-3<x<\frac53$

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