Q55 / 170 · Manipal (MET) 2021 · Mathematics

$\left|\frac{x}{2}-1\right| \lt 3$ implies that $x$ lies in the interval

  • Correct answer
    A
    $(-4,8)$
  • B
    $(-3,6)$
  • C
    $(-4,6)$
  • D
    $(-3,8)$

Solution

$\begin{array}{r}\left|\frac{x}{2}-1\right| \lt 3 \Rightarrow-3 \lt \frac{x}{2}-1 \lt 3 \\ -3+1 \lt \frac{x}{2} \lt 3+1\end{array}$ $\begin{array}{ll}\Rightarrow & -2 \lt \frac{x}{2} \lt 4 \\ \Rightarrow & -4 \lt x \lt 8 \\ \therefore & x \in(-4,8)\end{array}$

Hence, the correct answer is option: 'A'.

Relevant Questions