The solution set \x: x R, 3x-2 < x+2 ≤ 2x+6\ (Where R is set of real numbers) is : Option 1: [-4,2) Option 2: [-4,-2) Option 3: [-4,2] Option 4: (-4,2)

Answer: [-4,2). Solution: From 3x-2 < x+2 we get x < 2. From x+2 ≤ 2x+6 we get x ≥ -4. Intersecting the two gives [-4,2).

Algebra

Inequalities

Easy

applied

The solution set $\{x: x \in R, 3x-2 < x+2 \le 2x+6\}$ (Where $R$ is set of real numbers) is :

[-4,2)

[-4,-2)

[-4,2]

(-4,2)

✅ Correct Option: 1

From $3x-2 < x+2$ we get $x < 2$ . From $x+2 \le 2x+6$ we get $x \ge -4$ . Intersecting the two gives $[-4,2)$ .

2026: 22 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:

2025: 22 May Shift 1

The solution set of the inequation $4x + 3y > 5$ is

2025: 22 May Shift 1

If $\frac{1}{x^2} - \frac{1}{x} > 0$ , then $x$ lies in the interval

2025: 30 May Shift 1

If $\mathbb{Z}$ and $\mathbb{R}$ denote set of integers and set of real numbers respectively, then match List I with List II.

Choose the correct answer from the options given below:

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 :