The set $A = x : | 2 x + 3 | < 7$ is equal to

- 10 < 2 x < 4

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- 11 < 2 x < 4

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- 12 < 2 x < 4

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- 13 < 2 x < 4

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Solution

The correct option is A $- 10 < 2 x < 4$
$| 2 x + 3 | < 7 \Rightarrow - 7 < 2 x + 3 < 7 \Rightarrow - 10 < 2 x < 4 \Rightarrow - 5 < x < 2 \Rightarrow - 5 + 5 < x + 5 < 2 + 5 \Rightarrow 0 < x + 5 < 7$
which is equivalent to set $W$
so option $A$ is correct.

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