If 1/|x| - 3 ≤ 1/2, then value of x: Option 1: x (-∞, -6) (-3,3) (5, ∞) Option 2: x (-∞, 5) (5, ∞) Option 3: x (-∞, -3) [3, ∞) Option 4: x (-∞, -5] (-3,3) [5, ∞)

The answer is 'x (-∞, -5] (-3,3) [5, ∞)'. View full solution:

Algebra > Inequalities

Medium

applied

If $\frac{1}{|x| - 3} \leq \frac{1}{2}$, then value of $x$:

$x \in (-\infty, -6) \cup (-3,3) \cup (5, \infty)$

$x \in (-\infty, 5) \cup (5, \infty)$

$x \in (-\infty, -3) \cup [3, \infty)$

$x \in (-\infty, -5] \cup (-3,3) \cup [5, \infty)$

✅ Correct Option: 4

Related questions:

2026: 29th May Shift 2

The solution to the inequality $-12 < \frac{2x-1}{3} < 12$ is

2026: 21st May Shift 2

The solution set for the inequality $|5x-3| \le \dfrac{1}{5}$ is:

2026: 22nd May Shift 2

Match List-I with List-II

List-I: Inequation	List-II: Solution set
(A) $2(2x+3)-10<6(x-2)$	(I) $x\in(-\infty,3.9)$
(B) $\frac{2x-1}{12}-\frac{x-1}{3}<\frac{3x+1}{4}$	(II) $x\in\left(-\infty,\frac{-1}{2}\right)\cup\left[\frac{1}{2},\infty\right)$
(C) $\frac{x}{2x+1}\ge \frac{1}{4}$	(III) $x\in(0,\infty)$
(D) $\frac{2x-3}{4}+6>2+\frac{4x}{3}$	(IV) $x\in(4,\infty)$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

The solution of $\frac{7x+12}{x-9} < 4$ ; $\neq 9$ is:

2026: 30th May Shift 2

The solution set of the inequality $3x+4y<12$ is

2023: 22 May Shift 3

All points lying inside the triangle formed by the points (5, 0), (-1, 2) and (1, 3) satisfy :

(A) $3x + 2y - 18 > 0$

(B) $3x + 2y > 0$

(D) $2x - 3y - 12 < 0$

(E) $2x - 3y + 12 > 0$

Choose the correct answer from the options given below :