12. 12(3x5+4)≥13(x−6)

12. Given, 12 (3x5+4)≥13 (x−6) 62 (3x5+4)≥63 (x−6) ⇒ 3 (3x5+4)≥2 (x−6) ⇒ 95x+12 ≥ 2x−12 ⇒95x−2x≥−12−12. ⇒9x−10x5≥−24. ⇒− x*5≥5−24*5. x ≥–120. (–1) x (–x)≤ ( –120)* (–1) x ≤ 120. So, x ∈ (–∞, 120].

12. $\frac{1}{2} (\frac{3 x}{5} + 4) \geq \frac{1}{3} (x - 6)$

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Payal Gupta | Contributor-Level 10

9 months ago

12. Given, $\frac{1}{2}$ $(\frac{3 x}{5} + 4) \geq \frac{1}{3} (x - 6)$

$\frac{6}{2} (\frac{3 x}{5} + 4) \geq \frac{6}{3} (x - 6)$

$\Rightarrow 3 (\frac{3 x}{5} + 4) \geq 2 (x - 6)$

$\Rightarrow \frac{9}{5} x + 12 \geq 2 x - 12$

$\Rightarrow \frac{9}{5} x - 2 x \geq - 12 - 12 .$

$\Rightarrow \frac{9 x - 10 x}{5} \geq - 24 .$

$\Rightarrow \frac{- x * 5 \geq}{5} - 24 * 5 .$

x ≥–120.

(–1) x (–x)≤ ( –120)* (–1)

x ≤ 120.

So, x ∈ (–∞, 120].

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