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

The set A={x:|2x+3|

A
$D = {x : 0 < x + 5 < 7}$
B
$B = {x : - 3 < x < 7}$
C
$E = {x : - 7 < x < 7}$
D
$C = {x : - 13 < 2 x < 4}$

Solution:

Given set, $A = {x : | 2 x + 3 | < 7}$

now,

$\begin{array}{l} | 2 x + 3 | < 7 \Rightarrow - 7 < 2 x + 3 < 7 \\ \Rightarrow - 7 - 3 < 2 x < 7 - 3 \Rightarrow - 10 < 2 x < 4 \\ \Rightarrow - 5 < x < 2 \Rightarrow 0 < (x + 5) < 7 \end{array}$

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

Solution:

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