The inequality (5x - 2)/3 - (7x - 3)/5 > x/4 holds when Option 1: x (-4, ∞) Option 2: x (4, ∞) Option 3: x (-∞, 2] Option 4: x (-∞, 4]

Answer: x (4, ∞). Solution: The inequality is (5x - 2)/3 - (7x - 3)/5 > x/4 The LCM of the denominators 3, 5, and 4 is 60. Multiply every term by 60: 60 x (5x - 2)/3 - 60 x (7x - 3)/5 > 60 x x/4 20(5x - 2) - 12(7x - 3) > 15x Expand: 100x - 40 - 84x + 36 > 15x Combine like terms: 16x - 4 > 15x Solve for x: 16x - 15x > 4 x > 4 Therefore, x (4, ∞)

Algebra

Inequalities

Medium

applied

The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when

$x \in (-4, \infty)$

$x \in (4, \infty)$

$x \in (-\infty, 2]$

$x \in (-\infty, 4]$

✅ Correct Option: 2

The inequality is $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$

The LCM of the denominators 3, 5, and 4 is 60.

Multiply every term by 60:

$60 \times \frac{5x - 2}{3} - 60 \times \frac{7x - 3}{5} > 60 \times \frac{x}{4}$

$20(5x - 2) - 12(7x - 3) > 15x$

Expand:

$100x - 40 - 84x + 36 > 15x$

Combine like terms:

$16x - 4 > 15x$

Solve for $x$ :

$16x - 15x > 4$

$x > 4$

Therefore, $x \in (4, \infty)$

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 :

2024: 16 May Shift 1

The solution set of the inequality $|3 x| \geq|6-3 x|$ is :

2025: 15 May Shift 2

The solution set of $6 \leq -3(2x - 4) < 12$ , $x \in R$ is:

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) The solution set of the inequation $3x-6\le 0$ is	(I) $(3,\infty)$
(B) The solution set of the inequation $-5x+20<0$ is	(II) $[3,\infty)$
(C) The solution set of the inequation $3x-9\ge 0$ is	(III) $(-\infty,2]$
(D) The solution set of the inequation $8x+11>35$ is	(IV) $(4,\infty)$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(Inequality)	(Solution Set)
---	---
(A) $2x - 3 < x + 2 \le 3x + 5, x \in \mathbb{R}$	(I) $x \in (-1, \infty)$
(B) $\vert 2x + 3\vert < 7, x \in \mathbb{R}$	(II) $x \in (-\infty, 120]$
(C) $\frac{1}{2}\left(\frac{3}{5}x + 4\right) \ge \frac{1}{3}(x - 6), x \in \mathbb{R}$	(III) $x \in (-5, 2)$
(D) $\frac{\vert x + 1\vert }{x + 1} > 0, x \in \mathbb{R} - \{-1\}$	(IV) $x \in \left[-\frac{3}{2}, 5\right)$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

The solution set of inequality $3x + 5y < 4$ is

The inequality 5x−23−7x−35>x4\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}35x−2​−57x−3​>4x​ holds when

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when