Question

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

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

Answer 1

Answer: (C)

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