Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

If $\frac{3x-5}{6}+8≥4+\frac{2x}{3}$, then

Options:

$x ∈ (-∞, 19]$

$x ∈ (-∞, -19]$

$x ∈ [19,∞)$

$x ∈ [-19,∞)$

Correct Answer:

$x ∈ (-∞, 19]$

Explanation:

The correct answer is Option (1) → $x ∈ (-∞, 19]$ **

Solve the inequality:

$\frac{3x-5}{6}+8 \ge 4+\frac{2x}{3}$

Multiply both sides by $6$:

$3x-5+48 \ge 24+4x$

$3x+43 \ge 24+4x$

Shift terms:

$43-24 \ge 4x-3x$

$19 \ge x$

$x \le 19$