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  4. The set A = x: |2x + 3| < 7 is equal to the set

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Q. The set $A = \{x : |2x + 3| < 7\}$ is equal to the set

KCETKCET 2014Sets

Solution:

Given, set $A=\{x:|2 x+3|<7\}$
Now, $|2 x+3|<7$
$\Rightarrow -7< 2 x+3<7$
$\Rightarrow -7-3< 2 x<7-3$
$\Rightarrow -10< 2 x<4$
$\Rightarrow -5< x<2$
$\Rightarrow 0< (x+5)<7$