The solution set of the inequation, 2x - 3, ≤ 4 is Option 1: [1/2, 7/2] Option 2: [-1/2, 7/2] Option 3: [-1/2, 5/2] Option 4: [-7/2, 7/2]

Answer: [-1/2, 7/2]. Solution: The absolute value, 2x - 3, ≤ 4 means the expression (2x - 3) must be within 4 units from zero. For, A, ≤ B, the inequality becomes -B ≤ A ≤ B. With A = 2x - 3 and B = 4: -4 ≤ 2x - 3 ≤ 4 From the left inequality -4 ≤ 2x - 3: -4 + 3 ≤ 2x -1 ≤ 2x -1/2 ≤ x From the right inequality 2x - 3 ≤ 4: 2x ≤ 4 + 3 2x ≤ 7 x ≤ 7/2 Combining both results: -1/2 ≤ x ≤ 7/2 The solution set in interval notation is [-1/2, 7/2].

Algebra

Inequalities

Easy

applied

The solution set of the inequation $|2x - 3| ≤ 4$ is

$\left[\frac{1}{2}, \frac{7}{2}\right]$

$\left[-\frac{1}{2}, \frac{7}{2}\right]$

$\left[-\frac{1}{2}, \frac{5}{2}\right]$

$\left[-\frac{7}{2}, \frac{7}{2}\right]$

✅ Correct Option: 2

The absolute value $|2x - 3| \leq 4$ means the expression $(2x - 3)$ must be within 4 units from zero.

For $|A| \leq B$ , the inequality becomes $-B \leq A \leq B$ .

With $A = 2x - 3$ and $B = 4$ :

$-4 \leq 2x - 3 \leq 4$

From the left inequality $-4 \leq 2x - 3$ :

$-4 + 3 \leq 2x$

$-1 \leq 2x$

$-\dfrac{1}{2} \leq x$

From the right inequality $2x - 3 \leq 4$ :

$2x \leq 4 + 3$

$2x \leq 7$

$x \leq \dfrac{7}{2}$

Combining both results:

$-\dfrac{1}{2} \leq x \leq \dfrac{7}{2}$

The solution set in interval notation is $\left[-\dfrac{1}{2}, \dfrac{7}{2}\right]$ .

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Inequality)		LIST-II (Solution Set)
A.	$\vert 3x-5 \vert \geq 4$	I.	$(-\infty,-1] \cup \left[\dfrac{7}{3},\infty\right)$
B.	$\vert 3x \vert \geq \vert 6-3x \vert$	II.	$(-\infty,-4] \cup [2,\infty)$
C.	$\vert x+1 \vert \geq 3$	III.	$[1,\infty)$
D.	$\vert 2-3x \vert \geq 5$	IV.	$\left(-\infty,\dfrac{1}{3}\right] \cup [3,\infty)$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

The solution set of the inequality $\frac{2x+3}{x-1} < 0$ is:

2026: 31 May Shift 2

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

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.

List-I	List-II
(A) $5x - 3 \leq 3x + 1$ , $x \in \mathbb{Z}$	(I) $x \in (-\infty, -3]$
(B) $3x + 17 \leq 2(1 - x)$ , $x \in \mathbb{R}$	(II) $x \in (-\infty, -1)$
(C) $13x + 17 \leq 2(1 - x)$ , $x \in \mathbb{R}$	(III) $\{......, -4, -3, .......,0,1\}$
(D) $\frac{2x + 3}{5} - 2 > \frac{3(x - 2)}{5}$ , $x \in \mathbb{Z}$	(IV) $\{......, -4, -3, -2\}$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

For the inequality $3-2x \geq x-32$ , which of the following are true?

(A) When $x \in N$ (set of natural numbers), the solution set is $\{1,2,3,\dots,11\}$ .

(B) When $x \in I$ (set of integers), the solution set is $\{-\infty,\dots,-3,-2,-1,0,1,2,3,\dots 10,11\}$ .

(D) When $x \in R$ (set of real numbers), the solution set is $(-\infty,\infty)$ .

Choose the correct answer from the options given below:

2025: 13 May Shift 2

If $a > b$ and $c < 0$ , then which of the following is NOT correct?

(A) $ac < bc$

(B) $a + c < b + c$

(D) $ac > bc$

Choose the correct answer from the options given below:

The solution set of the inequation ∣2x−3∣≤4|2x - 3| ≤ 4∣2x−3∣≤4 is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The solution set of the inequation $|2x - 3| ≤ 4$ is