Q. The set of values of $x$ satisfying $2 \leq |x - 3| < 4$ is
A) $( - 1,\ 1\rbrack \cup \lbrack 5,\ 7)$
B) $- 4 \leq x \leq 2$
C) $- 1 < x < 7$ or $x \geq 5$
D) $x < 7$ or $x \geq 5$
Explanation
(a)
Since, $2 \leq |x - 3| < 4$
$\Rightarrow \ \ 2 \leq x - 3 < 4$
Or $2 \leq - (x - 3) < 4$
$\Rightarrow \ \ 5 \leq x < 7$ or $- 1 \leq - x < 1$
$\Rightarrow \ \ 5 \leq x < 7$ or $- 1 < x \leq 1$
$\therefore\ \ x \in ( - 1,\ 1\rbrack \cup \lbrack 5,\ 7)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.